Least connections doesn't need shared state between the instances, but it would need shared state between the load balancers if you had more than one for sure.
You're totally right, I glossed right over errors. With PEWMA and weighted round robin you can make instances incur a "penalty" for serving errors, which can help you isolate bad servers. It would have been fun to visualise this, definitely.
It also strikes me that it might be interesting to model least connections with two or three LBs with and without such shared state.
My instinct is that you'd still get most of the advantages even with each LB keeping its own independent connection counts, but given the number of times I've fired up a profiler and gone "wait, seriously, -that-s the slow part?!" I'd suggest nobody believes me and measures it instead.
You're totally right, I glossed right over errors. With PEWMA and weighted round robin you can make instances incur a "penalty" for serving errors, which can help you isolate bad servers. It would have been fun to visualise this, definitely.