[OneFunFellow]

From a technical perspective you're correct. I can't think of any holes in your argument.

From a non-technical perspective I would say convenience. A link is a click or a tap that would open a new window and walk me through the reset process. A password-in-email I would have to highlight it, copy it, open (or move to) another window/tab, then paste it then go through the "change password" process.

A link is a much smoother user experience.