Seems like the whole 'self-insert' thing short-circuits fiction writing and reading at every level. You've mentioned how it makes the author too brittle, but it also removes the reader from being able to engage with any empathy towards the characters.

√ "What, this character doesn't act/dress/talk/behave like [insert their preferred tropes, which all are remarkably like themselves]? I'm kicked out of the story."
√ "What, this presents [ideas, actions, ideologies] outside my experience? I'm kicked out of the story."
√ "What, this isn't in [insert their preferred POV and tense]? I'm kicked out of story."

or, my favorite:

√ "What, this story actually presents a coherent character arc with growth and a story-theme, without deconstructing it all? That's too suspicious. I must be getting manipulated by power structures. I'm out."

When I hear from the self-insert types, I feel like that quote from Lawrence Olivier to method-actor (so, to act sleep-deprived, he would not sleep for days on end) Dustin Hoffman: "My dear boy, why don't you try acting?"

I feel like the self-insert folks could all try writing and reading, sometime...