It would be pretty trivial to paste without formatting but still auto-parse links. Many apps do the link parsing on the client side, so it's not a formatting concern at all.
That's fine if the text you're copying spells out the URL, but often it will be just a word(s) that are hyperlinked, so if pasted as plain text the software you paste into has no idea there was a URL linked at all.
(But I too wish plain text pasting was the default more often.)
How would that work in the case where the link display text is not the address? Normally pasting without formatting discards the fact that some text like “download other file” is a link.