Always. Main reason I cut something is I want to paste the hostname into a terminal so it can be an argument of whois or dig or traceroute or whatever, in no case have I ever been glad of the scheme prefix.
Isn't more common to paste to a utility that uses the prefix like curl or wget? Or pasting into a chat? Besides all of those tools could just strip out the prefix, while there's no way to add the protocol to a domain name.
More information is better, so the URL shown in the browser should include the protocol. Consistent behavior is better, so copy/paste should only include text that is actually highlighted.
