As far as I've heard, the hopes for Cloud TPUs in general are that people will think it's an amazing service worth paying for.
The hopes for TFRC are more complicated, as you might imagine when a company is giving away free stuff, but one of them, I'd put in the "long-term benefit altruism" category: It's quite hard to do some kinds of machine learning research in academia, because it can be fantastically expensive. We just blew $5k of google cloud credits in a week, and managed only 4 complete training runs of Inception / Imagenet. This was for one conference paper submission. Having a situation where academia can't do research that is relevant to Google (or Facebook, or Microsoft) is really bad from a long-term perspective, and one thing TFRC might do is help make sure that advances in deep learning continue at a rapid pace.
From watching the rate at which my deep learning colleagues get swallowed up by industry, I think it's a very valid concern, and I'm very supportive of all of the industry efforts we're seeing to try to address this. It's good for the entire research ecosystem.
(There are undoubtedly many other reasons, such as those noted below by minimaxir, but this is the one I personally feel the pain of.) Disclaimer: I get paid by Google part-time to do work related to this, but this is not any kind of official statement. The pain-of-ML-in-academia bit is purely from my hat as a CS professor.