As someone who once studied literature, I would be cautious about imagining too direct a link between biography and interpretation.
I've only read about half of the first volume of Goethe's extremely long memoir (I keep setting it aside and then occasionally coming back to it), but he does not give the impression of someone who had an unhappy childhood -- indeed, much the reverse. He seems to have been a fairly wealthy, even spoiled son of an upper-class family, who even during the wartime French occupation of Stuttgart (IIRC) had access to private tutors and a relatively comfortable life thanks to his father's position as a city official of some kind. As a young person at least, he also seems to have had a markedly cheerful, optimistic, even buoyant personality, as far as I could tell. He was kept mostly at home as a young child, but once he was older and the war was over (IIRC), he did start spending more time out and about on his own around the city, and claimed (though I haven't read other accounts to compare) to have spent a good deal of time with friends from all walks of life.
And just in general, he lived a long life and met a lot of people, so he could certainly have been aware that some people abused children, whether physically or sexually or verbally, even if he was never abused or an abuser himself. That's part of what makes a good literary writer: observing other people and turning real life into fiction by imaginatively altering it; as opposed to a historian or scientist, who would simply report observations as fact.
To get back to the poem: literary interpreters would probably remind us to practice close reading just of the words on the page. The father in the poem doesn't abuse the child himself; instead, he's oblivious and fails to protect him from the Erlkönig. Again, that doesn't mean we can jump to the conclusion that Goethe must have had an abusive tutor or other acquaintance, but something like that could also be within the range of possibility.
But does it really matter if he experienced a real instance of abuse himself, or heard about such a case from someone else, or just imagined it based on things he had seen, heard, and read, the totality of his life experience? Again, he's not a reporter, he's a poet. What makes the poem worth reading is what it means to readers, not what facts may or may not lie behind its conception.