Also, w.r.t. linear communication, CBC Casper[2] has the ability to come to consensus on a blockchain with, in the limit (and in the optimal case), a single message per block that is finalized. It uses essentially the same form of pipelining that HotStuff does, but to the extreme (at at the cost of a much longer time for blocks to be finalized). Full disclosure: I work on CBC Casper, so take what I'm saying with a grain of salt.
[1] https://dahliamalkhi.wordpress.com/2019/04/24/flexible-byzan...
[2] https://github.com/cbc-casper/cbc-casper-paper/blob/master/c...
The 1/3 bound is without any synchronicity assumptions; with strong synchronicity assumptions you can get to 1/2. This seems strictly better than PoW (no liveness at all in an asynchronous network, and 1/2 with synchronicity assumptions).
In terms of implementing PoS, most BFT algos have traditionally scaled poorly (HotStuff which is linear in communication costs relative to the number of nodes/validators is very recent). In addition, going offline for validators, even accidentally, hurts the network and slashing PoS schemes often have uptime requirements. Validators also need to have the infra to be hidden and not DDOS'd.
tl;dr, Proof of stake is still decently centralized, but a lot of work is being done to scale it.