They used to make it work with waxed paper. There's no reason why that can't be used for a large proportion of food packaging again.

That's just a different non-biodegradable petroleum product: https://en.wikipedia.org/wiki/Paraffin_wax

A lot of food grade wax is carnauba.

I assume that anything sold today as waxed paper has plastic in on it, but I don't really know.