Here's my opinion as a former professor who taught biostatistics, epidemiology and public health.
Assigned, graded homework is completely unnecessary, even at the college level. I almost never assigned homework because I had the utmost confidence in my abilities as a teacher. Homework is for students who have teachers who can't get the lesson across to their students in the classroom.
And for the record, math doesn't necessarily require a high degree of repetition, either. Fast, accurate, rote math requires repetition. On the other hand, if you've taught almost every student (there will always be duds) in a high quality way, they'll be able to figure out the principles involved when asked to on a test.