So I could set all members with zero posts to members of the 'newly registered users' group. Then I could set the permissions of that group to be the same as non registered members.
Isn't it means screening rest of the forum from newly registered members? If so, this is a bad idea, I think. When I registered here I was attracted by content which I could read despite my zero posts status. After this I found appropriate to introduce myself here. If I considered this forum uninteresting, I would never have done that.
If I correctly understanding your idea, I think, after start of this new rule you'll greatly reduce inflow of new members and Nutters will become closed elitist community which is doomed to death without fresh blood. This is a dead end road.
Then once they have posted and introduced themselves they will automatically become 'registered members' and have full access to the forum.
Ask yourself: why new member should want to introduce himself on a forum most of which is closed for him? He must have a very strong motivation for that.
I vote for free and open community. If you want to build a sandbox for close friends, do as you want. But if you want to attract new people there is no need for additional restrictions and barriers.