How important is a good rack?

"I'd be very interested to hear accounts of people
doing serious ABs comparing a "merely
competent" rack (say like my homebrew rod and block)
with a SOTA rack, say like a Finite Elemente, which costs
10 times more."

I went from Flexy to ikea lack to Finite elemente. I
guess that is like a/b/c. I wasn't serious, though, but I
did not have to be. The lack and finite are both much
better than the mdf-baced flexy, which was the heaviest
and stiffest. (Stiff in relation to the legs with
least stiff and heaviest shelves).

"What I was wondering about whether investment in
racking yields cost commensurate improvements comparable
to other elements in the chain, once the fairly modest
"threshold" I suggest has been reached. My
speculation is that for many of us, the money might be
more noticeably placed elsewhere."

I disagree because I do not believe its possible overcome
the problems of a bad rack elsewhere. I am also not
putting my stuff on the floor, especially since my stereo
is in my living room.

There's racks and there's racks with vibration control. One gets your equipment off the floor, the other does that while reducing distortion. Some of the latter are more effective at distortion reduction than others. Devices that are highly effective at vibration control and look great, such as those from Silent Running Audio or Harmonic Resolution Systems, command top dollar. Audio room infrastructure (acoustics, power, vibration control) is a necessary condition for realizing the sonic value of electronics and speakers.
 

Racks are a clear case of "horses-for-courses". Some manufacturers e.g. Grand Prix Audio, will insist on knowing what the various loads on the rack will be so that they can customise it by tuning it.
Praiseworthy though this approach may be it only deals with synergy at a simplistic level (i.e. no real-world AB testing with operational equipment)

Turntable support synergy is so unpredictable that the simplest mechanical features can radically alter the sound. I doubt that there are any guarantees that an esoteric table costing megabucks would even top a group table in a 5 or 6 way face-off against bargain priced opposition.

How does an equipment rack remove distortion?

I know what you mean by not wishing to put the things on the floor. Everyone is like that. But when you go to the shows many of the best sounding rooms have the equipment on the, uh, you guessed it. The floor. It's easier to control what's going on.