You don't need PAXOS, RAFT, or CURP to implement a key-value store. Those are distributed state machines, all you need is distributed state.
That means you don't need a leader election. You don't need a leader. You don't need any round trips. You don't need coordination.
PAXOS was the only game in town for many decades, but there are better ways to do this now.
But, if CRTDs allow independent operation, don't they check the high availability box?
What they don't do is give you a global linear ordering. But you don't need that in a key-value store, and you don't need that in most distributed computing.
People keep reaching for PAXOS and RAFT when they don't need it. It's pretty rare that you need a distributed linearization.
The earliest knowledge I have of this is Generalized Paxos, but I believe there's more recent work with the likes of Egalatarian Paxos. I think there were even some CRDTs that mixed strong consistency and weak consistency.
https://github.com/xline-kv/Xline/blob/master/curp/tla%2B/cu...
https://github.com/xline-kv/Xline/tree/master/curp/tla%2B
¹warning, I skimmed and ctrl-fd for "leader election"
And KV stands for Key Value.