And what about mixing both your ideas? A user can register and mainly read different threads to get started before shitposting, and after some days/weeks start posting. But when doing this, he is most likely logged in.
In the event of one (or many) brand new account that do not post anything and are not logged in in X days, that ban you are talking about could be feasible
If he/she wants to post/ask something, he/she needs to register, but in this case a post will follow the registration pretty soon.
What happens if the brand new account (without any post) is banned because of inactivity after a while (e.g. 2 weeks)? Nothing special, the user won't lose anything but the username itself because it's banned and not deleted.
We could delete the inactive brand new accounts (without any post), in order to help users to register the username again if they were deleted because of inactivity but they really want to post with the choosen username in the future, this could be a second chance for those who are not account farmers...