Well, I always thought that my basses had a medium action at best. Turns out it's really quite low. As I use flats, I don't mind a bit of clank from the frets, so digging in isn't too big a deal. And they're lovely and easy to noodle on.
I would find it unpleasant if the action was too much higher, but it's what you get used to, I suppose.
Certainly surprised our Beedster when he got my Frankenjazz. He mentioned the action wasn't right for him when he got it, and my immediate thought was that it was too high. But in fact, it was much, much too low for his playing style. Not a problem to correct, of course!