[nerdponx]

Zsh is different, although I'd be surprised if this wasn't the Bash behavior.

It doesn't make sense. If you do

    alias e=vim

it's not like Vim opens when your shell starts.

The only way to have a "precomputed" alias is to get the quoting wrong, and leave $() in double quotes instead of single quotes, meaning it will be evaluated before the alias is even assigned.