I'll even be charitable in order to simulate the existence of school/teachers/books: training from the start gets 2KW. But gameplay still gets capped to 20W.
Of course, you can hire people, and that has a well-defined cost, so it does all come down to money again.
We are comparing machine intelligence vs human intelligence.
It can be said that with more computational power, you can raise intelligence. Human brains consume the most power relative to body size than any other animal.
Also, mobile phones have Internet access, so there's no reason the algorithm has to run on the phone itself. It could run on TPUs in the cloud. It's common for many games to have server-side components. Though this isn't even necessary except maybe if Magnus Carlsen wants to play it.
But, I don't think a lot of people would pay for that vs. having a program that just runs on there phone and still beats them. So, in practice without a significant subscription fee you are going to be limited to cellphone hardware.
PS: In practice most games take about as much computing power from a server as a chat app as companies need to pay for that hardware. Remember 1,000,000+ X get's big unless you keep X very low.
It'd be like in a discussion about SpaceX's BFR designs to colonize Mars, someone comes in and questions why they're using retropropulsion since the requisite control systems are infeasibly expensive for amateur model rockets. It's a completely different discussion.
Otherwise the only takeaway is this failed to improve the state of the art.
So, the only case where chess performance per $ matters is if you are only going to ever use that hardware to run chess. In every other case which is the vast majority of the time you care about diffent metrics.