Ok, but then your email client should be smart enough that if, for example, you quote two bullet points from a list it doesn't quote them as
<div class="quote">
<li>Second</li>
<li>Third</li>
</div>
Without the surrounding `<ul>`. Luckily Thunderbird is smart enough to do this. I don't know about other clients.
<div class="quote"> quoted content </div>
It's far better than trying to keep count of how many ">" are in play, and deal with the vagaries of soft linebreaks and hard linebreaks and wrapping of plaintext.