It's kind of the Nick Drake syndrome. Why kill yourself because folks don't love your songs? Chances are you won't love their songs, either,. Just do what you do and don't worry about what people think.The upside is, you can't know that answer until you put it out there where someone else can listen to it; sneak it in, then give the songwriting credit to a stage name you make up.
I think part of the problem is that we think that what we write has to be as good as the best stuff others have written, that we like most to listen to- or it's "no good".
Like you, I never take credit for songs when I perform them, and I don't let anyone else give me credit, either. I can't function unless I take my ego out of the equation. The songs aren't about me. They're about themselves. The day they start to be about me, they'll start to suck, and I'll sell all my gear and take up selling vacuum cleaners, which at least are supposed to suck.
Just lost a songwriting competition, by the way. A relief, though I would've loved the prize money. More good news is that the song I entered was better than the three ego-drenched winning songs. A lot better.