This will not be a popular answer but Linkedin and others are effectively bots so the closest thing to painful would be that the end users never see it. That means adding regex/wildcard filters for subjects and keywords in the body. Adding anything to slow down their connections will likely just trigger an error on the account saying the email is invalid and could lead to account lock-outs.
Even better if there was a shared github repo and associated addon people could use to filter these emails but there are so many different mail clients that it would become quite a project. Probably just a shared list of regex/wildcard patterns would suffice. This concept would have to become popular for them to notice their engagement emails are not increasing revenue. Spam pays. Until spam does not pay this will be a pain for all of us.