1. The mods didn't ban him and just only deleted all of his spam posts (which is bad because he could repeat his bad habit again, who knows?)
Nope, I think that account was already banned by now. All of it's posts are deleted because Moderator nuked it and banned it as well. There's no way s/he can post again except if this user has multiple accounts.
Simply reporting the spammers we can not do anything else,
You're right, that's the only thing we can for now to survive this battle against shitposters.
We need a restriction on registration
I've suggested several ideas about restrictions on registration before but seems like all of those ideas of mine are nothing but stupid. Putting restrictions in registration won't fix the problem except if you're idea is different from mine (it has possibility). What's in your mind about this restriction?
the ability to send messages for new accounts,
I think it's possible to send messages to new accounts. What's with this anyway?