All I can guess about this common grammatical error is that people write what they hear. Let me explain what they hear, then:
In other words, a contraction of should have, might have, etc. What they think they hear is this:
"I should of gone to the store earlier."
Gone is a (conjugated) verb, therefore nothing can be of it or belonging to it. There is no "of gone." Although maybe if you're a country singer, you can come up with a song in which the lyrics go something like "It's the slow sad sound of gone." Go for it. Have fun. Just please don't write "should of."
"I should've gone to the store earlier."
"I should have gone to the store earlier."
But I didn't, so we're still out of milk. Maybe I'll do that now.