Having a sort order is immensely preferable when you're joining multiple sequential rows at once. The optimiser can create a pseudo-partition for your join, and constrain its reads to that. Especially on spinning rust (or I/O constrained systems), you're also reading multiple sequential pages in a stream off disk, which gives a big speed boost compared to random reads.

Without that ordering, the index is 'dumb', and has to find all your rows one by one in its structure. Admittedly it's not as much of an issue for SSDs, but it does still impact performance.