If it is true that performance scales infinitely with compute power - and I kinda hope it is, since that would make superhuman AI achievable - datacenters will always be smarter than PCs.

That said, I'm not sure that it does scale infinitely. You need not just more compute but also more data, and there's only so much data out there. GPT-4 reportedly won't be any bigger than GPT-3 because even terabytes of scraped internet data isn't enough to train a larger model.