This won't work because it does not distinguish between spam and legitimate bulk mail, of which there is lots. Or do you want to bankrupt Facebook?
Spam is already a solved problem, pretty much. If you have a spam problem outsource your mail to Google. Job done.
Bulk physical mail pays postage, albeit at a reduced rate, so how would this somehow bankrupt everybody?
If I lost my password for this forum, guess how I get a new password.
Yes, by mail. So if I want to screw a boardadmin, I just request 1000 times a day a new password.
Or I ask an email for every post done in a topic, nice if 100 people do that and get 500 mails a day.
See how long it takes before the board is bankrupt.