Particularly with solo songwriting efforts, the point at which you finally realize how the completed song should sound, but not too far beyond that point, is the sweet spot. For me, that's when there's this fresh "je-ne-sais-quoi" still in the air, and I like to hear it. Yes, listening back to some of my completed, released recordings makes me hear a few minor things here and there I wish I'd done a bit differently, but for the most part, I don't mind them too much.
When I get ready to play any of them live long after the record came out, I'll perhaps fix a couple of phrasing issues, or even slightly rewrite a couple words, but the bottom line is they were close enough to the overall vision at the time to be deemed release-worthy according to my admittedly low standards at the time. Further, I hereby argue that "almost complete" state can be a better listen, because you hear the potential a future, more professional recording could have, and that's exciting. Indeed, many a fan who have reviewed my music tell me things along those lines - that they can envision how the song would sound on a famous artist's album done in a pro studio, etc. I take those as nothing but compliments.
Practice doesn't make perfect for me, with either the songwriting or recording part. Performing the song all the way through once live with a guitar and vocal is usually necessary to envision how the final recording should sound, but that's all. The less I rehearse, the more organic it is, and the less likely I am to get bored, which can curb the passion. I want people to hear the passion, the excitement of the song being newly written and me enjoying playing it for one of the first times all the way through and being psyched that it works and sounds like a keeper song to me. Even in a multi-track recording environment, I like to limit each track to only 2 takes, maybe 3 for the lead vocal.
That said, very often I get a kick out of "nailing it" on the first take, whichever instrument or vocal it is, which to me just means no majorly noticeable mistakes. The vocal should convey the emotion of the singer liking the song and you should be able to hear the satisfaction with the fresh creation coming together into a final arrangement in a style that the singer/songwriter "imagined" or heard in his head. Same with the instrumental tracks - as long as there are no glaring errors, its always better to not keep doing take after take, or heaven forbid do the splicing or comping techniques to get it all perfect.
If I took advantage of all that modern music equipment and studio technology has to offer, I'd feel like I was cheating too much. There's something about somewhat handicapping myself and intentionally not having the best tools that keeps things challenging and satisfying for me. I'm doing it the hard way, yes, and no, I don't want it to sound too good. That says something about me, and my music, and you might not get it, and you might not like it, and that's okay. It's not for everyone.
Books and documentaries about famous artists like Dylan or bands like the Beatles will often convey something along the lines of the fact that the early takes in the recording studio are often the ones that make it onto the albums, despite many more being recorded afterward. So, there is proof I'm not alone with my preference.
I can imagine the same principle being applied to live performance of music as well. When a band is learning a new song, and the arrangement is decided on, and the finished product begins to reveal itself, there is magic in the air. Everyone has just learned their parts, and they're getting "tighter" as they rehearse it, and this is both exciting for the band and the listener. When a band is at the end of a long tour that used a setlist with many of the same songs every night, you might be able to pick up on their boredom or lack of passion as compared with the first few times they played it in front of an audience. That said, a band like the Grateful Dead may have been an exception.
So even though trying out songs in front of an audience to get their reaction and feedback before recording in the studio is never a bad idea, if you don't do anything about that feedback, pure repetition alone won't make it any better. You've got to take into consideration the insanity definition of trying the same thing repeatedly while expecting a different result. Another factor to apply is that it is important to trust your fans.
If you trust yourself and are true to yourself with the music you choose to record & release, you know your own quality standards are there, and thus, you know your fan base will appreciate it. Take the guesswork out and trust your gut, which is the same as trusting your fans' good judgment. If you're an artist like me, you don't want your music to ever sound too perfect anyway, and neither do your fans.
There is a growing spark and a spirit that builds momentum and reaches a creative peak as seeds of songs germinate into complete flowers, but the trick is to capture them near those moments "before the bloom is off the rose."