I've read Must blockquotes contain paragraphs or must paragraphs contain blockquotes?, so I see why blockquotes can contain p elements themselves. However, I feel that this, in principle, shouldn't exclude that a blockquote can happen to be in a p elements; after all, the ps inside the blockquote are the paragraphs relative to the quoted text, but why couldn't the quoted text be part of a bigger paragraph of the containing document?
See the following
<p>This is a paragraph</p>
<p> This is another paragraph: with a <blockquote> in it
<blockquote>some long quote</blockquote>
which (notice the lower case <i>w</i>) I write something about here, so it makes sense I'm not starting a new parapgraph, imho.
</p> <!-- this very editor highlights "p>" in red -->
No.
The start of the blockquote element will implicitly end the p element.
This is why the end tag for the p element is shown is red: There's no matching start tag for it because the element is already closed.