My experience has been there is no correlation between skill at teaching and skill at research; maybe the two are even anti-correlated. To some extent, this is an artifact of the selection process for professors, but I think it's partly because there's a real tradeoff between spending effort on research vs teaching.

In some cases, an excellent researcher even has cogent papers but is absolutely abysmal at lecturing and in person teaching skills.

Peers are very important, but from talking to others, it's harder to know where you will get good peers than you would think. Even 1st tier universities will have majors dominated by students whose primary interest is in maximum grades with minimum work and where cheating is rampant. You've got to either get lucky (I did) or put in some leg work to find smart students who are actually interested in learning and doing things right.

I think how much rote memorization is encouraged or required is strongly dependent on the field. Pre-med students will sometimes memorize their way through calculus; a professor I knew once described it as "grimly impressive".

Teaching is a skill like any other. While I don't think the two are anti-correlated, you're going to find good teachers and bad teachers, no matter how good they may be at their other duties.

And I would gather you find more bad teachers than good, but that's true of many spaces from IT to sports.