Why do we say "On purpose" vs "By accident"?

Solution 1:

I think it is a question of idiomatic usage, on purpose is an idiomatic expression which dates back to the latter part of the 16th century:.

• "by design" is attested from 1580s.

Its earlier foorm was "of purpose (early 15c.)" probably from the French "de propos".

(Etymonline)

Note also the expression : accidentally on purpose:

Origin

• The first printed record of this phrase that I can find is from The history of the famous preacher Friar Gerund de Campazas, by José Francisco de Isla, 1772:

  • Tell us what is Modesty of Voice, for you happened accidentally on purpose to drop this word, and I don't rightly know what it signifies.

The Phrase Finder