I think one place where this discussion gets bogged down is in the distinction between repetition and practice. Experts spend vast amounts of time in what I recall the Cambridge Handbook refering to as "mindful practice".
There is a difference between doing AoPS problems or doing sheets of cookie cutter work. If the work is not in the child's zone of proximate development there is unlikely to be any benefit. So when looking at school work the question is whether it is vital practice or mindless repetition. In this view repetition is unlikely to be beneficial and is always suboptimal.
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The other issue is that the problems parents are usually objecting to are highly algorithmic. I think there is a valid concern that excessive overuse of drill can reduce the extent to which the material is generalized and available for creative use. I've read studies looking new math(CSMP) vs traditional. CSMP taught more varied approaches to elementary math so with similar class room time had less repetition of the traditional approaches. In follow-ups the CSMP kids had similar computation scores to the traditional kids but had significantly higher outcomes on novel problem solving tasks. I don't want to get in to a debate about new math :); I've seen similar studies in the sciences when richer curricula are used.
The issue is not that repetition is harmful per se. Its that repetition crowds out other much more beneficial work.
