Й is absolutely linked with и, and it arose as alphabetic distinction from it. It appeared and disappeared for certain periods; in Russian it reestablished as a letter only in 20th century. It is still commonly collated with И in indexes and dictionaries.

> "Ё" is a bit more tricky, but nevertheless — there's no another letter in Russian alphabet we could put umlaut on and get the result similar to putting umlaut on "е".

This is a bizarre distinction: diacritics in natural languages aren't supposed to be freely recombinable.