Part of the problem is a poor (or insufficiently DWIM) implementation of rich text copy-paste. If I copy text that has some parts bolded or italicised, that is indeed "the damn text I copied". But the fact that the source website happens to be 12pt blue Verdana should not override the fact that I'm writing an email in 11pt black Arial.
In many cases I do not particularly care whether an email is in 12pt blue Verdana or 11pt black Arial, I absolutely care about there suddenly being a big blue word in the middle of my otherwise-consistent paragraph.
So neither "rich text" nor "plain text" are really correct: often plain text is good enough, but sometimes it's easier to correct the rich text.
It's probably a hard problem to solve generically. Word has a little popup when pasting where you can select how you want that paste to be applied: Just text, text with its original formatting, or formatted text, adjusted to the document styles. So far I've used all three, so I guess there's no answer that fits all use cases.
In many cases I do not particularly care whether an email is in 12pt blue Verdana or 11pt black Arial, I absolutely care about there suddenly being a big blue word in the middle of my otherwise-consistent paragraph.
So neither "rich text" nor "plain text" are really correct: often plain text is good enough, but sometimes it's easier to correct the rich text.