According to most sites TOS, when we write our posts we give them basically full access to do whatever they like including make derivative works.

2 points:
1 - I'm generally talking about companies extracting data from other websites, such as OpenAI scraping posts from reddit or other such postings. Companies that use their own collection of data are a very different thing.
2 - Terms of Service and Intellectual Property are not the same thing and a ToS is not guaranteed to be a fully legally binding document (the last part is the important part.) This is why services that have dealt with user created data that are used to licensing issues (think deviant art or other art hosting services) usually require the user to specify the license that they wish to distribute their content under (cc0, for example, would be fully permissible in this context.) This also means that most fan art is fair game as licensing that content is dubious at best, but raises the question around whether said content can be used to train an AI (again, intellectual property is generally different from a ToS).

It's no different from how Github's Copilot has to respect the license of your code regardless of whether you've agreed to the terms of service or not. Granted, this is legally disputable and I'm sure this will come up at some point with how these AI companies operate -- This is a brave new world. Having said that, services like Twitter might want to give second thought of claiming ownership over every post on their site as it essentially means they are liable for the content that they host. This is something they've wanted to avoid in the past because it gives them good coverage for user submitted content that they think is harmful.

If I was a company, I wouldn't want to be hinging my entire business on my terms of service being a legally binding document -- they generally aren't and can frequently be found to be unbinding. And, again, this is different from OpenAI as much of their data is based on data they've scraped from websites which they haven't agreed to take data from (finders-keepers is generally not how ownership works and is more akin to piracy. I wouldn't want to base a multinational business off of piracy.)