So I looked into this a bit and…

it appears to be based on whether a word is using Latin or Greek as its etymological basis, for words pertaining to feet.

In Latin… it is ped-… but in Greek… it is pod-.

… And, you are correct, English has a mish mash of both.

But also, a lot of English words referring to children use the Greek derived ped- or pedo- to refer to… children.

…Which is why in British English, the spelling ‘paed-’ is used, to minimize this confusion.

But us clever Americans dropped that, rofl.