> There aren't any "spaces we haven't formalized"

Suppose that space of N points is partitioned into M relevant subsets, for now we assume of the same size. Then random sampling hits each of those subsets in O(M log M) time, even if we don't know what they are.

This sort of partitioning is long talked about in the testing literature, with the idea you should do it manually.

> what work is being offloaded

The need to write that program for explicitly enumerating the space.