Why do you think blockchain would be immune from regulatory capture?

Regulatory capture requires:

• Having a party which is trusted to administer a system
• Influencing the actions of that party to your benefits

Decentralized blockchains don't have the first requirement there. There is no trusted party to influence. Blockchains are trustless systems, in order to make them do something they are not designed to do, you have to influence not just one people or ten people, but at least half the people in that system, and even then, there are limits on what they can do because the people you didn't influence are still running the old version of the software and will simply ignore whatever your influenced people are doing since it isn't valid network activity. You can take your military and go around the world and hold guns to people's head, but unless you hold a gun to all the people's heads all the time, you can't make the blockchain do anything it wasn't designed to do. The term for this is a 51% attack and, at least in the Bitcoin ecosystem, the only thing you could achieve is a double-spend (spend the same BTC twice). You can't spend money that isn't yours, because that's an invalid transaction and will just be rejected out of hand by the older non-malicious version of the software.

Hasn’t the general story of crypto-adjacent items thus far been one of immense gains for the few and immense losses for the many?

That is one way to look at it. There are certainly many grifts and scams in the crypto world, just like there are elsewhere outside of crypto. They're bad. On the contrary, Bitcoin, for example, has faithfully kept to it monetary policy and all its promises now for 15 years running 24/7 365 without a single hack or hour of downtime. It has resisted attacks from nation-state actors. This is powerful stuff. Crypto doesn't have to have a "rich get richer" outcome, it can also be a tool to lift people out of poverty and give them autonomy, particularly the billions of people, with a B, who lack access to stable banking infrastructure or who have national currencies so corrupt they are basically useless and as a result, they have no ability to save money outside of the day's earnings. One other way this is true is that in a fiat economy the government prints money, right? The US aims for 2-3% inflation, this is its economic policy. Every time they print money, they devalue your dollar because those new dollars go to somewhere else. Your dollar is like a share in the US economy that went through a stock split, but instead of ending up with two dollars, you still have one and somebody got the other one. This is theft on a massive scale, not only from US citizens, but it's how we tax the global south and enforce US imperialism abroad. Our system of debt, regulated through institutions like the world bank, is all based on the dollar. But the economy is also growing right? So your dollar is becoming more valuable even if it's a smaller share of the total number of dollars? Even if those things even out (which they don't, the inflation rate is deliberately set higher than this), you are still having the difference in that value stolen from you. With Bitcoin, if you own 1BTC, you will always have 1BTC, and your share that represents of ALL BTC will stay the same because Bitcoin has a fixed supply. So when Bitcoin's economy grows, those benefits aren't given to whoever is operating the money printer, they are given to whoever holds Bitcoin. Same as when the economy shrinks. That, out the gate, is a more equitable system than fiat currency.

And isn’t the historical rule of statistics/maths such that it is clear that these “objective” measures are actually very easy for the powerful to manipulate for their own ends? Lying with statistics is very easy to do, for example.

Bitcoin isn't just a graph somebody drew. It's not located in a single place where somebody can just go in and draw a new line. It's decentralized, all over the globe, running according to a set of rules that can't be broken. Many have tried, the best hackers and brightest minds in the world have tried, it's not doable. This is because Bitcoin's protocol is based on cryptographic protocols which are as real as temperature or anything else physical. They are based on splitting things up into a mathematical space where trying every possible combination to break them would cost much more than the reward for doing so. As an example, in Bitcoin the way you spend it is by broadcasting a transaction to the network which is signed by your "private key" it looks like "I, Bob, want to send 1BTC to Alice - Signed, Bob". The private key is a number, it gets plugged into a math equation. If you don't have that number, you can't sign the transaction, so your transaction won't be valid, no nodes will relay it, and it never makes it into the blockchain. The money doesn't move. This means if you have the private key, you can spend the money, if you don't, you cant. But wait, couldn't you just guess the number? No. The number space you would need to go through is so vast that it's difficult to wrap your head around. If every computer on earth suddenly dedicated itself to guessing this number, they would all do so for tens of thousands of years before they ever got the correct one. That's what people are talking about when they say Bitcoin is based on math and physics. It's not just hyperbole.

What prevents Peter Thiel-types from framing and shaping the code that governs whatever blockchain-connected system emerges?

If Peter or anybody else releases a new Bitcoin client, they have to convince everybody else in the world who uses Bitcoin to use it. That's what prevents it. Thousands of eyes of some of the world's smartest coders looking over it, and yes, investments banks who need the Bitcoin protocol to remain stable and usable. You yourself can look at the code if you want, it's all public. In this way, blockchain technology is truly democratic. People can choose which blockchains to interact with, and even within those blockchains, which part of the protocol they want to follow. Is there some layer between the programmer and the user? Of course. Users have to understand what choice they are even making. Why should I use Litecoin instead of Bitcoin? Somebody has to communicate those differences for people to understand them. This is a problem in all political/legal/economic systems to some degree. Which gets us to your next question.

And what prevents Cambridge Analytica type entities from manipulating public opinion such that only the “right” kind (the evil kind) of blockchain is the one that “spontaneously” becomes the natural choice of the grassroots?

This is absolutely a threat, you are 100% spot on here. One key problem that blockchain can potentially solve, and I will skip over for now, is the centralization of social media platforms. Nobody should have the power to put the thumb on the scale that hard. But back to your question: Blockchain technology, just as it can be used for good, can be used for evil. CBDC (Central Bank Digital Currencies) are one of these kinds of threats. They would enable the government to see every transaction you to, in real time, and be able to block or intercept transactions at their whim. They also create a massive repository of everybody's financial data, ripe for hackers. And unlike decentralized systems like Bitcoin, they have central points of failure, and hackers can exploit them.

I would argue many nation states and other actors are indeed doing these kinds of PR campaigns right now. There are some very powerful people, like banks, who benefit from their rent-seeking behaviour and ability to print money without consequence, they do not want to see Bitcoin become the dominant global currency. Convincing people not to use Bitcoin is dollar-for-dollar the most effective way to attack the Bitcoin network. Nonetheless, year after year, on average, if you draw a trend line, Bitcoin continues to grow despite these efforts. It doesn't matter how you measure it: number of nodes, total market cap, liquidity locked in lightning, etc. I'm sure you have seen your share of headlines declaring that Bitcoin is finally dead, but nonetheless each year it is not. And while the value of a bitcoin, how much somebody will pay for it, will fluctuate with time, so long as the internet exists at at least a few computers are running the code, you will still always have 1 BTC and you will still be able to transfer it just as Bitcoin has promised you.

The error of the Leninists was, among other things, thinking that because they had an exceptional understanding of how historical economic structures have been controlled and shaped by the powerful that they, therefore, would themselves be able to use this knowledge to create a new type of state that was exempt from these failings. That obviously did not occur. And I fear that the STEM types who understand blockchain, and who generally have sincerely good intentions, will similarly be blindsided by the realities and insurmountable corrosive strength of global capital

You may very well be right about this, only the future can tell.

Which doesn’t mean that no better world is possible - it is. It just means that I don’t think we can trust a computer code to impartially distribute a truly moral justice throughout the country/world. Because the oligarchs will seize and corrode such a code and subvert it to solve their own ends. And I don’t know how you stop them from doing that given that their wealth gives them practically unlimited power

Their wealth doesn't give them power in the Bitcoin system because math and physics, I hope you can see that now that it's been explained a bit more. We can't trust computer code you are right, but we can trust networks of people who write, review, and run that code. At least, we can trust them in so far as we can trust anybody to do anything.