To hijack the thread a bit ...
Occasionally, I have played with a pianist who reharmonized on the fly.
I don't have big enough ears to follow a lot of what he did. So, I had to lay out some of the time. At times, I could hear what he was doing or I could manage with 3rds and 7ths, if he was just adding tensions, but, a lot of the time, he was modulating key, so it didn't work. I couldn't follow it by ear. And, he didn't do the same thing every chorus.
Even when I could hear, say, that he reharmed a long ii-V by simply modulating up a half step -- he wasn't predictable with it. At best, I'd have to wait and hear what he did.
Interestingly, I recently attended a workshop taught by two players (keys and guitar) whose names you might know and I asked them if, when the other guy started playing "out", if they always knew what he was doing. They both said no. The kb guy said that he'd try to pick up a single note of what the guitar was doing and try to extrapolate as best he could.
I understand the goal -- to have well trained ears, listen hard and cooperate. I'd say the skill level involved in doing that effectively rises when you add a second chord instrument. It's much easier to play when there's no piano.
Even guitarists often acknowledge that the piano comes first and the guitar needs to somehow color and enhance. In that situation, you have to try to figure out the pianist's harmonic content while phrasing with the rhythmic content, while keeping the guitar from making mud with the frequency spectrum and keeping track of the soloist's harmonic and rhythmic content -- and not forgetting about the bass and drums. I guess it's a little easier than that sounds, but maybe not much easier.
At the intermediate level or playing a tune that not everybody knows well, there will be somebody reading and that throws another bit of debris in the gears.
It's my impression that the skillset where you know the same 500 or so tunes that all the other players know -- and you don't care what key you're in -- well, that's less common than it used to be.