That has some problems. If you limit the total number of attempts globally then the feature is effectively disabled, every botnet and script will blow through the attempt budget and real users can't use it. Global limits and IP address limits are not useful, and because we're assuming the user is unauthenticated (using the password reset), we have no other way of distinguishing good traffic.
Captcha comes to mind, but that's a cat-and-mouse game in the age of machine learning (not to mention actual humans working for a bad actor). Cloudflare seems to be on the cutting edge with their newest challenge mechanism, but good vs bad is somewhat distinct from human vs script.
My wife was in charge of security at MySpace back when MySpace was still a thing and there was one occasion that the MySpace team was manually feeding images to a suspected human acting as a bot. As I recall it became clear to both sides that there were humans on the other end and it ended with a picture of a scantily-clad woman and a response of “very funny.”
