> But at what point do we run out of training data?

Isn't the training itself very dependent on each algorithm. Even if you somehow gathered all the plausible training data, you'd have to run it through again for most improvements of your system.

But there are trends to look at in this direction: changes in the training that make it much, much faster; And processors which become more effective (fewer of them needed).

So anyway, very long term, sure. For now, doesn't seem to be a problem.

For that matter, for now, there is not only building new data centers, but also upgrading existing ones to the more efficient processors.