The answer is that’s just the way English is. Exactly 1 is singular, everything else is plural (mostly).
“On accident” is American English, as a British English speaker I’d consider it a grammatical mistake. The same goes with “I forgot it at home” and similar constructs. However they’re correct American English.
There are a few things like this which really sound weird to a British ear.
Another example is the use of "Write" in the sentence, "I wrote them". This is completely wrong to the British ear, which would be "I wrote to them".
> I forgot it at home
As a non-native speaker, I find the sentence equally disconcerting, but it leaves me wondering what one would use to say something to that effect.
I think the reason that "accident" is confusing is because of "I did it on purpose". As a fellow British English speaker, I would never say "by purpose!". By and large, I think that US English tends to be more logical.