We don't need a subset of HTML. Actually, we need Markdown emails. You can format stuff that needs structure, but not abusively so (no blinking marquee banners in eyesore colors), it is sufficiently compatible to plaintext that you don't even need the text alternative mime object. It is also more compact than HTML.
And before somebody says "won't fly", all those fancy new "will replace email someday" messengers use markdown or some parts of it's formatting.
You know what? We had that. Markdown was modelled after it.
I would also state that Markdown itself is completely unsuitable for the purpose. You’d need to design something new which might look very similar to Markdown, but which would have basically no shared behaviour with even CommonMark as regards parsing, since you don’t want HTML to be a thing. Markdown itself is seriously compromised by its HTML basis.
I can’t actually think of a single comparatively-mainstream messenger that uses even a variant of Markdown; rather, they use their own lightweight markup languages <https://en.wikipedia.org/wiki/Lightweight_markup_language> that are very clearly incompatible with Markdown. (It’s also often a frontend editing feature that gets turned into something like HTML after that.)
text/enriched has been around for decades, and supports basic font styling (bold/italic/underline, color, font face, font size) and that's basically it.
Actually, text/markdown exists as well. However, the definition of markdown syntax is, um, less than precise: https://daringfireball.net/projects/markdown/syntax (the text/markdown RFC literally has a parameter to indicate which flavor you meant by markdown!). And it incorporates HTML too, FWIW--legal HTML fragments are legal markdown as well. Honestly, markdown's million variants makes the HTML support landscape look uniform.
And before somebody says "won't fly", all those fancy new "will replace email someday" messengers use markdown or some parts of it's formatting.