The consensus among distributed systems people without a financial stake in it seems to be that practical proof of stake remains an open problem. Obviously no one that owns SOL or DOT or ADA or whatever is going to say that, but I’ve looked hard for a scalable, secure, reasonably cost effective PoS L1 and come up empty so far.
There isn’t a Cardanos consensus protocol per se: there are a family of them under the umbrella term “Ourobouros”. In production it’s the BFT variant which is sort of a warmed over tendermint or algorand.
The more ambitious variants are very mathematically rigorous but axiomatize a wall-clock oracle, as well as in some cases mathematically-interesting but practically absurd assumptions about synchronicity.
Hoff has deployed his private fortune doing (among other, uh, things) serious research on distributed Byzantine consensus.