They are useful for exploratory maths. If someone has an idea for a theorem "All semigroups with properties X and Y are of type Z", while an automated proof might be major work, a simple check of all semigroups up to a certain size is trivial, and a counter-example doesn't require a complex proof.

However, for numbers of the size I was looking at, storing them is impossible. We were just interested in how many there were (which wasn't known, and we don't know how to calculate without enumerating them through search).