In my mind the problem proof of work solves is how quickly new blocks can be generated [...] There is actually no real point of rate limiting the creation of n

In my mind the problem proof of work solves is how quickly new blocks can be generated [...] There is actually no real point of rate limiting the creation of new blocks, why not generate them as fast as possible and therefore execute transactions as quickly as possible? This certainly needs some more thought, you do not want miners spamming empty blocks or blocks full of their own fake transactions, you can not provide a fixed block reward, and whatnot. But in general the mining rate limit is a limitation and not a feature. Proof of work has nothing to do with that, any system that can encourage everyone to agree on the next block does the same prevention of double spend. Sure, proof of work establishes consensus and any consensus algorithm could be used. But Bitcoin is anonymous, so you do not know how many parties are there that need to agree and therefore a simple vote based consensus protocol does not work. You have to prevent a malicious user from casting a million votes and changing the consensus branch as they please. How do you do that? You make casting a vote hard, you make them, for example, waste a lot of clock cycles to do so.