There are at least 300 species from multiple phyla that feed on humans. We might also consider those species that feed on our livestock, although such an action would have less ethical urgency.
It isn't impossible that other species might eat them, but given their baroque life cycles it seems quite unlikely that any other species depends on them for survival. But sure, if people decide to start with tests on isolated tropical islands, I won't argue.
>> there are many cases in the natural environment where parasites like this are the vector limiting overpopulation
Can you provide a couple of examples? I'd be interested in looking into this further to see how that works. Obviously, predators are a different category, and fill an important niche in the ecosystem, but I was unaware that species classically considered "parasites" performed a similarly important role. For example, ticks on moose seem very different from wolves hunting them.
https://phys.org/news/2020-08-parasites-important.html
This is the link above which made me overconfident to easily find on the web many examples of such natural regulations. But I could not find a lot... what is more easy to find is mathematical studies showing the effect on populations.
Here is one study considering the potential implications of parasites eradication:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5222570/
For some particular examples, the red grouse is a bird whose population follows periodic cycles, and the cause is a parasite. Removal of the parasite smoothed out the population variations. You can imagine other species (plants or animals) whose own population cycles would be adapted to the old cycles, and these species would be impacted by the smoothing out of red grouses.
Link: https://www.jstor.org/stable/4694?seq=1
More generally, when a parasitic regulation disappears, the next in line would be resources regulation, that is the species starves when the food is scarce, and thus the population plummets. That could lead to a very different population dynamics (as the red grouse example shows, but there can be situations where the graph is sharpened instead of dampened like here), and because of that one or several species can disappear.