[1]: More precisely, the work they need to do doesn't scale linearly with the allocation rate as is the case with non-moving approaches. Of course, arenas are sort of degenerate moving collectors, so they also display the same effect, but they can't always be used.
The way this works is that you allocate in the young generation with a pointer bump, and to free memory you compact (move) the surviving objects, which make up a small minority, a few times and then promote (move) them to the old generation (where you either manage memory with the same technique or a different one). And so the total amount of moving is not high (objects either never move or rarely move), and what you end up with is essentially two heaps, one where the allocation rate may be high but you can completely negate all the extra work by increasing the size of that heap, and one where the allocation rate is low. This ability to, optionally, not double the amount of work when the allocation rate doubles is what gives moving collectors their efficiency (and that you can bump-allocate in virtually all cases).
Of course, it's possible to come up with programs where objects do move a lot (or there's some other common work), e.g. programs that don't exhibit the behaviour of the generational hypothesis, but the point is that in a very large class of programs, this technique is hard to compete with.