If I really end up having to read an HTML email those can be displayed "inline" using a text browser such as w3m. If the HTML is mostly text it works pretty well, for instance: https://svkt.org/~simias/mutt-html.png
If however it's image or css-heavy and doesn't work well in text-only form there's still the option to tell mutt to open the email in your web browser. Of course in this case there are security implications so it's probably best not to do it from untrusted sources.
One concern is that I'm letting through all web bugs and, perhaps, outright malicious HTML. If anyone has a solution for that, something like filtering the HTML, I'd love to hear it.
No, but HTML emails, 99% of them, are just plain text in an HTML markup. You won't miss garish colors or font choices.
As for embedded images etc, you can still view them with plain text mail clients (as attachments).
~/.muttrc: alternative_order text/plain