The kindness of that feeling if not tempered by hard-nosed pragmatism directly collides with the reality of what is actually achievable.

There are 8 billion people in this World, most of which have a lower or much lower "chance to live a life worth living" than the even the average Western.

If everybody outside the West that could have a better life in the West was allowed to come over what would happen is that the place would end up with lots of people with a far lower level of formal education (so less capable of doing the high value jobs that produce more wealth in the West), with different customs (causing lots of friction) and who do not know the language (again a problem for them to be productive alongside the natives), and its capacity to create wealth would most certainly collapse on a per-capita basis - essentially too many people coming over from places with very different quality of life and education system would kill the very golden eggs goose that justified them coming over in the first place.

There are limits to how much we can help without endangering the very thing that allows us to help, which means we have to look at it from a hard nosed pragmatic perspective. As I see it, it breaks down into 3 things:

• Triaging: we can't help everybody so lets start by helping the ones with the most need (hence why I explicitly mentioned Refugees in my last post). In fact I think we should be actively going out and looking for those needing the most help and helping them, not waiting for the strongest and with the most capability to find the money to pay for it (so, not the ones with the greatest need) cross over on some boat.
• Give a man a fish and you will feed him for a day, teach him to fish and you will feed him for a lifetime: we should be investing in helping people to help themselves were they live, such as with Healthcare and Education. If the objective is indeed "do our best to ensure that people all over the world have a chance to live a life worth living" then realistically for them to immigrate over is often the least effective option to achieve that, mainly because of all the 2nd and 3rd order negative effects from it when done in very large numbers without time for integration.
• Crack down on all those Westerners who. for personal upside maximization, are helping make the countries were those people live much worse than they should be. I'm talking Financiers and Weapons Dealers helping Dictators and the Corrupt in many countries stay in power and enjoy the money they steal from the rest. I'm also talking more indirect guilt, such as the pollution produced in the West (including Global Warming) that affects poorer countries far more or even the one produced in poorer countries whilst trying to make things to sell to the West.

A genuine will to "ensure that people all over the world have a chance to live a life worth living" means we have to find solutions that actually work in the context of objective reality, not high-moral-horse-ridding simplistic takes on things.

I also believe we have a duty to do our best to ensure that people all over the world have a chance to live a life worth living.

Which if you take a holistic view also includes things like not brain-draining developing economies. That's going to become an even bigger issue in the future as source countries complete their demographic transition and themselves start to shrink.

In an ideal world, immigration for economical reasons just shouldn't be a thing, and immigration for opportunity reasons rare, like joining a specific research institute as a scientist. Immigration should happen for curiosity, for love, such kinds of things.

create infrastructure in the countries of origin and help towards stable political systems

That is so much easier said than done. Without sane politics in place over there investing in infrastructure means the local grifters pocket everything. Stability alone is not sufficient, plenty of kleptocracies are plenty stable. Many are even democracies. It's always easy to blame colonialism but colonialism didn't destroy South Africa's electricity grid: The ANC did, and the ANC alone. What do you suppose we do against that kind of thing? Send cannon boats up rivers, like in the good ole days?

combat climate change

Definitely important, but also not sufficient on its own. It's just the crisis of the day, plenty of other sources of trouble in the world.

so in effect the political rightwing is very much causing the problems that they want to be racist about.

Let's not wash the hands of the left clean by missing that in practice, it's not addressing the issues either. The left is usually right in its material analysis, the right is generally (and frighteningly) right in its emotional analysis -- that's their thing, they slavishly resonate with people's worries -- neither is any good at actually fixing shit. If the left was, then the right wouldn't have anything to resonate with, or it would occupy itself with makeup trends or whatever. I agree, painted on eyebrows are a danger to what is good and proper, to civilisation itself.