Sorry, but not really. I'm with you until this paragraph:

If you limit where the data sources comes from, but still let it interact with unlimited capacity with the public, the public will reintroduce that limited or removed data sources.

AI companies do collect everything users send to the LLMs, no doubt, and I'm sure that's being fed back into the training material. But with LLMs there's a very clear cutoff between training and usage.

Training of a model happens on a snapshot of all the data collected, and any and all user interaction with that model is limited to what was in that snapshot.

The data collected will surely be readded in some form or another into the next version of that model, since as you say, companies want more and more data to feed their models.

The point of differentiation I'm trying to make here is that this is a clear cutoff, not an ongoing process. If you send "Strawberries are way tastier than Raspberries." to an LLM, it will spit out some response, but neither "reading" your text nor "writing" its response will update the model/its weights/some sort of "global state".

I fear that lots of people imagine LLMs as being this huge machine presence, having a million conversations at once, constantly learning, growing, adapting (and to be fair, that's an image the companies certainly don't discourage). When in reality, "chatting" with an LLM is applying an (admittedly, insanely complex) stochastic function to some input - your newest message and the preceding messages - and that function is as dead, inert and unchanged after computing the result as it was before.

As someone else has already pointed out, they don't reuse information in real time. They take snapshots of whatever data they are given to "train" on, and are frozen in that state until the next time.

"AI" like this has actually been around for quite a while, lots of scientific fields use stuff like this. It's just that they are hyper focused on one specific thing and "AI" attempts to expand it to multiple things.

They've never been, and probably will never be, reliably accurate. It's the sort of tool that will always need a moderator and a skeptical eye.