In experiments involving study participants, why are some studies allowed to only have a small number of test subjects?
Although large samples produce more robust results, small samples are not completely devoid of usefulness - they're just more likely to be wrong. As long as the reader keeps this in mind, there's nothing fundamentally wrong with publishing these small-sample studies.

Further, sometimes you just cannot get enough samples to make an assertion with confidence. Examples:

GW170817 was a one-of-a-kind neutron star merger event. Since the rate of neutron star mergers isn't well-known, one could easily wait another five years and not get another sample (plus you'd need hundreds of samples to make the kind of statements you're looking for).

The Berlin Patient - there's no cure for AIDS. Even if this single case were a fluke, it's still worth reporting since it's a signpost telling researchers where to look.

Habitability research - The question of whether aliens exist captures the public imagination. Like it or not, we have to approach the problem from what we know, and we know only one planet with life (i.e. sample size of one). You could of course just decline to work in the field until we've discovered several hundred alien civilizations, but then you could be waiting forever. Plus with no idea what to look for, observational astronomers would have a much harder time finding these civilizations.