What is Jeremias 31:34 affirming?

Some Protestants use this as saying that there will be no need for a Magisterium.

Let's look at the verse with previous verse:

But this shall be the covenant that I will make with the house of Israel, after those days, saith the Lord: I will give my law in their bowels, and I will write it in their heart: and I will be their God, and they shall be my people And they shall teach no more every man his neighbour, and every man his brother, saying: Know the Lord: for all shall know me from the least of them even to the greatest, saith the Lord: for I will forgive their iniquity, and I will remember their sin no more
[Jeremias 31:33-34]

Now, certainly each man, even each child (and not just each Apostle) who is forgiven will know God and know what to do.

But by contrast with what?

Does it say "and priests shall teach no more the rest"? No, it says:

And they shall teach no more every man his neighbour, and every man his brother, saying: Know the Lord:

In other words, what ceases is a discipline of mutual correction. We are not dealing with a condemnation of the magisterium but of things like Holiness Churches and Islam, and before both obviously the OT Judaism and its quasi-continuation today. One man, not a priest, is saying to the other "know the Lord!" and then that other man, also not a priest tells the first man "know the Lord!" ... that's what is ceasing. When a Catholic is exposed to a climate of intense "fraternal correction" he has not chosen, he notices this kind of attitude as non-Catholic. And sure, in the New Testament, there is no continuous need for it, there is more like a free initiative within God's law.
/Hans Georg Lundahl