If you make an app that does this well, and makes it easy to share the recorded clip to the iNat app (if feasible, with date/time/location pre-filled as when importing a photo), I would definitely use it, and probably be willing to make a purchase for it.
Right now I’m using Birdnet, which does keep a running buffer (complete with live sonogram) when you have it open AND on the home screen, and in record mode, and allows to you to choose what to keep by making a selection on the sonogram. But if it could be doing that in the background, that would be much more useful. And clips shared from Birdnet to iNat loose the date/time/location data, even though Birdnet does record it.
I agree with others that this might feel like bloat if included in the iNat app itself (though I probably would use the feature if no other app had it). But I think the privacy concerns are based on a misunderstanding - this is easily solved by making it an opt-in only feature, not to mention that mobile OS’s these days don’t allow microphone access in the first place unless you’ve specifically enabled it.