>Wikipedia already lists 2 paxos variants that have byzantine security One of those mentioned is Fast byzantine consensus (FBC) [1]. FBC provides an optimal algorithm for a 2 phase commit system w/ byzantine agents. But FBC requires that each correct process sends a message to each other. This is O(n^2) and does not scale. Bitcoin (specifically, others differ) maintain some of the invariants with extremely high probability over time. High enough to be useful. In exchange, bitcoin's network scales much better. Really, it just needs O(n) messages to confirm a transaction.

Of course, PoS like Ethereum's takes much inspiration from byzantine paxos. But I wouldn't call this a solve problem, and crypto has innovated in this space. We can just debate whether or not the innovation has been worthwhile ;).

[1] https://www.cs.utexas.edu/~lorenzo/papers/fab.pdf