If people see a message saying "x has tried to contact you, do you wish to allow them", some of them will say yes. So spammers will continue to spam just as hard as they always have.
Also, considering how easy it would be to spoof "x", they could probably make people click "yes" a significant amount of the time.
'"get-viagra-cheap-now" has tried to contact you, do you wish to allow them'
- the spammer has just succeeded in putting their message in front of you. If you had 500 of those per day, it would constitute spam which would again need the same filtering.
Directly, it doesn't. However, I can block your certificate., or better, I can block the CA signing certificates that represent either businesses I don't want to talk to or people who don't really exist.
Whilst I don't generally believe governments should intervene in the internet, this is one area they could intervene in. They could act as a certificate authority.
Of course, CAs will make mistakes, but they can revoke certificates when things go wrong.
You can also currently block IPs, domains, URLs and specific message content. There are even globally distributed lists of such things.
This is already how we manage to block most spam on the edge. What you're proposing is just a small iteration on the existing defences. An expensive one, which wouldn't work unless you managed to get everyone doing it at the same time.
Also, considering how easy it would be to spoof "x", they could probably make people click "yes" a significant amount of the time.