Even by 2007, it was hard for anyone to improve, and after 2013 or so, the
very best centaurs were reduced to basically just opening book preparation
(itself an extremely difficult skill involving compiling millions of games
and carefully tuning against the weakness of possible opponent engines), to
the point where official matches have mostly stopped (making it hard to
identify the exact point at which centaur ceased to be a thing at all).
3 has been empirically disproven at this point, I believe?
gwern on “centaurs” (humans playing chess with computer assistance):