Do you think it stems from an over-reliance on sheet music in the initial stages?
That's a very good question, and one I hadn't considered. There may be something to it.
The counterargument might be that beginners in band or orchestra start on sheet music too, and many are totally dependent on it forever. So, I don't know.
I have a few thoughts.
One is that piano students if they practice at all practice alone and never are forced to contend with their peers. A beginner band in middle school sounds horrible, out of tune and wrong notes, but they're playing together from day one. They don't practice either in the early stages
Another is that piano lessons are traditionally taught that way ignoring the stumbles, mostly because, well, tradition. But also maybe because fluency is not the priority for teachers, and they know 99% are just not going to get it anyway, so they fight the battles they can win. And maybe if you're a teacher and you hear stumbling rhythm 40 hours a week you don't notice it either.
And then there are those who think metronomes produce robotic playing and avoid them like the plague, for themselves and their students. The horrors!
It could also be that in our haste to get to harder music we are always playing pieces we can't do fluently, so we just accept it.
I would think of all the instruments, piano is the one the lowest percentage of students ever succeed in playing minimally let alone well. Of course it's also the instrument the most students are forced into unwillingly, so that might have something to do with it.
I do not allow my handbell students to play notes late, ever. If we have to do it at quarter speed we still learn it in strict tempo. I accept bad tone but not bad time.