I did a number of room EQs in my day, and -- if the system was
properly set up, and the room had decent acoustics to begin with
(ie, little or no slap echo, minimal wall reflections, etc), a
careful EQ would _drastically_ improve the sound.

Uh huh, and such rooms exist _where_?
Show me a living room that does NOT have reflections
causing enormous standing waves and nulls.

I overstated the case. However, if a room is reasonably well-damped (which
is not hard to do; some rooms are already that way), even conventional
multi-band analog EQ works extremely well. Such rooms do not have "enormous"
peaks and nulls.

You are right in saying that EQ basically corrects the room's steady-state
problems. It doesn't do much for "temporal" errors. But if the room isn't
too live to begin with, the steady-state correction results in a major gain.

I speak from experience, not just theory.