> You are true, but this solution could avoid the network

I don't think this is a network problem. Different apps/clients/relays will use different filters for prevent abuse. Some will be more welcoming, others more restrictive.

> Firsts day/weeks action of the spammer that will determine if he is annoying...

Don't think this works. If you give the benefit of the doubt to new users, spammers will have it as well, which means they'll consume resources and then after one week they'll generate a new key and start again. There is an asymmetry in their favour, which is bad.

Thanks for this convo, lots of ideas