`-eq` is for arithmetic comparison; `=` is for string comparison. They don't do the same thing, and it's unsound to uniformly replace either with the other.
The dangerous thing here is that an undefined number of contexts exist where Bash treats strings as arithmetic expressions, which can contain arbitrary code despite not being quoted for expansion. `-eq` is just one example of that; others have linked other examples.
(This is all for case #1. With case #2, `[` and `test` are also susceptible so long as their builtin variants are used.)
