My MUA (Mutt) can launch any editor you like for composing mail. I use Vim, but it would work equally well with Emacs, nano, or whatever you prefer. Mutt is not alone in this regard.
The point is, you don't have to have embed your MUA inside of your text editor in order to use your editor for composing mail. There's nothing particularly wrong with that approach, but it's not the only way to get that benefit.
I agree you don't have to, but if the interaction gets more pervasive, such that the points of interface become many, it can be easier to just implement it in the same environment. If you just want to edit mail in vim, that's one thing, but if you want to be able to use commands in the mail editor to contextually interact with the rest of a mailbox (highlight a URL and search your mailbox for other occurrences of that URL, or add an email address to your address book, to take simple examples), it becomes more like the IDE case. Either you have to implement the IDE in the editor's scripting language (the emacs approach), or you need to call out to a number of special-case Unix tools to implement each of the hooks (the vim approach).
I write all my work e-mail in GNU Emacs and use the Emacs VM mailer.
Because it's all inside Emacs, text from other contexts -- code, shells, mailboxes, and compiler and tool output -- can be accurately and quickly pulled into the messages you compose, improving the content and reliability of what you're saying in mail.
For example, if I want to use a complex identifier from a source file I've just looked at, I can autocomplete it (M-. or find-tag) quickly from a substring. I can choose autocompletion suggestions simultaneously from all contexts.
Obviously, copying and pasting regions from those other contexts is much more immediate too.
This is in addition to the advantages of having a familiar and powerful editing tool for formatting, tidying up messages, trimming unnecessary content, etc.
The point is, you don't have to have embed your MUA inside of your text editor in order to use your editor for composing mail. There's nothing particularly wrong with that approach, but it's not the only way to get that benefit.