As we're starting to see, it was mostly Intel not keeping up, actually. Moore's law is mostly holding up till today, and probably for a couple more years before we really have to switch paradigms.
The definition of doubling performance every few years stopped holding up a while ago. The formal definition of doubling the amount of transistors somewhat holds up, see the huge increase in core counts in recent years, but that doesn't benefit most applications much. Incidentally cloud providers are billing by core count so adding more cores doesn't help the bill.
Nope. It's just that GPUs carried the mantle. If you have a massively parallel number crunching application you should bite the bullet and port it to GPU, and you'll see a truly massive FLOP/$ increase. And unlike processors GPU performance is still rising 35-45% per generation, although that will slow if NVidia gets too far ahead.
Also, if your goal is to get optimal cost/FLOP and you are computing pretty much constantly then you shouldn't be using the cloud, to be honest. If you are IO limited or if you have burst use then maybe, but for cost/FLOP the kings are still consumer GPUs and Threadrippers, by very far and large.