My point is, with the puzzle difficulty getting higher and higher, wouldn't we need equipment that actually solves a single hash faster? Or is that not a factor?
What matters is the GH/s display in your miner software. Nobody cares if that is achieved by massive parallelisation or massive increase in clock speed (which means solving a single hash faster). Over the long run, both will happen.
Right, the time-to-hash for any single hash attempt doesn't matter that much. Everyone is in a race to find a nonce that solves the criteria for the difficulty of the current block, and everyone is attempting different nonces. If everyone counted from "0" and incremented from there, and there was a fixed integer that solved the "puzzle", then the fastest hasher would always win. But that's not how it works. The nonce that will solve the puzzle depends a lot on the header of the block you're solving, which is different for each node, plus I suspect each node starts at a random nonce position in an attempt to not duplicate work with other nodes.