Blocks Where Trees Fail

Because blocking has better cache locality and the asymptotics on real hardware follow the memory hierarchy: a block is one contiguous scan. You gain an $O(\log n)$ effective bound for that locality.

Because the aggregate need not be decomposable and the update need not have a composable lazy tag: a block can simply be rebuilt or brute-forced. You pay $O(\sqrt{n})$ per operation for that generality.

Because $O(\sqrt{n})$ beats $O(\log n)$ below roughly $n = 10^6$ once constants are counted: a block scan is one flat loop with no pointer chasing. You gain real speed up to that size.

Because a segment tree cannot apply an update to a whole range at all, only to a point: a block can absorb the range and defer it. You pay $O(\sqrt{n})$ per operation for that generality.