Comment by stochastimus

As OP noticed likelihoods often do show up in a comparative context. In that context one is asking which thing or sequence is most likely to occur by chance relative to another, under an (over simplistic, sure) IID assumption. In practice, the ordering of such things is often (hand-waving, sure) robust enough that, given no other information than the marginals, it is useful. So I think OP almost answered his/her own question: they are often quite useful in a comparative context and with no additional information.