I have started to figure out that “reading lots” of scores with different musical styles, and not following the rule I keep seeing in this forum, which can be summed up as this - “read through a piece once, keep going, and don’t correct mistakes”. I find my ability to read music increases if I play a piece several times over the course of 1 or 2 weeks. I feel like this produces a better result than reading through a piece once, and only once.
I don't see any conflict.
All students benefit from learning to sight-read without stopping to correct mistakes and keeping the beat going regardless (whether or not they do exams, whether or not they ever play with others, or accompany), but when learning new pieces, of course they would correct their mistakes - as I mentioned earlier about how I get all my students to sight-read their new pieces in front of me without stopping, then play through again, but stopping to correct every mistake.
Which, incidentally, was how all my four teachers taught, all the way from beginner to advanced.
Some would say that playing without correcting mistakes gets you in habit of performing, when you have to keep going no matter what, short of a complete breakdown. You can develop that skill by playing duets, or any ensemble playing where you learn quickly that there is no slowing down, or stopping, unless everyone needs to restart.
Actually, not many students get an opportunity to play in ensemble. How many adult students know a fellow pianist who wants to play duets with them? Or would their teachers want to spend valuable lesson time doing that?
But they might well be asked at some stage, when they are more experienced - for instance, a distant relative might visit next Christmas, and, knowing that you have been learning piano for five years, bring Silent Night in an easy arrangement and ask you to accompany everyone at the party.
They would be very disappointed if you can't sight-read without stop-starting with mistakes, losing your rhythm, throwing everyone off course.....
Isn’t musical note-reading fluency the goal that most of us are pursuing? So why not try to learn the correct notes and rhythm with as many pieces as possible. These pieces don’t need to be taken to the next level unless you decide you want to study them in more depth.