I thought that too, but thinking about it, Horikoshi would've come up with at least the names and quirks of the parents while making the students. Quirk inheritance matters, and you don't want to write yourself into a corner trying to figure out something that makes sense, right? Plus you need explanation why the parents didn't become heroes but their kid did.
I always figured Bakugou's quirk was going to end up being revealed as completely mutated, unrelated to whatever his parents had, because of how surprised and elated he was when he first showed it off at school.
We know quirk users get their powers 4 ways:
A straight passage of quirk from 1 parent to child
A combination of the parent's quirks to child
A mutated ability. Either a quirk a child receives that is different from the mother and/or father's quirk or a quirk child born to quirkless parents
A very rare passage type quirk. Two are A40's give and take ability and A40's brother's give ability.
If Deku was born with a quirk he should have had his mother's ability to attract objects, his father's ability to breath fire out of his mouth, a combination ability like controlling fire, or a whole new quirk.