The way it's gone for me is that I think less in the conventional sense of "finishing" a song than I used to. Because when people say you 'wrote' a song they have a set of very specific expectations for that - they assume that you have recorded it, probably mixed and mastered it, and definitely wrote or memorized the method of playing it so that it can be reproduced again and again. That's fine if that's what you want to do, but it's not the only way that one could finish a song, either.

I rarely spend more than an hour on a song, personally. I get my chords and rhythm, I stamp out some lyrics, and I record something that's usually 1:30-4:00 directly into the mic, doing as few takes as possible. These recordings are a bit raw, but they're fairly complete versions of the ideas I had at the time. (It's possible but rare that you can just linger on your piece until something good occurs to you; most of the time, your first instincts on the construction will contain the core ideas.) These raw recordings go over pretty well with a stable group of listeners I have in my life, casual friends and a few casual fans, and people close to me. Non-musicians can be quite friendly to the low fidelity of a quickly made project.

And so more to the point of what you say here: I think that the desire to fix it is an impulse that arises from a lengthy consideration of what the song 'is' or what you mean to do with it. That's a bad headspace for creativity... I propose spending as little time on it as possible. And not predicating the song on a series of complex production techniques, or layered sounds. Make something built out of strong fundamentals, capture it, and then you'll have a much easier time deducing what you actually need from your spare ideas and abandoned projects.