There has been some talk. But not nearly to the same extent as in Sweden and Norway. In Norway the monarch is no longer also head of the State Church. Not sure off hand how it is in Sweden.
I think one of the reasons is that in comparison to Norway, much fewer Danes identify themselves as Christians and let alone feel they have a particular affiliation with the State Church. I think it is much more common in DK to have personal interpretation of Christianity, where the State Church is not that necessary and as such who leads it, is really not that important either.
Those who don't care or are atheists have simply signed out of the State Church.
Another reason is that the current system works fine, so why fix what ain't broken?
A third reason is probably comparable to why the Danish monarchs still have a very specific Constitutional role, (Laws must be signed in order to be valid. All power comes from the Majesty and so on.) is that most people actually like the idea of the politicians having to be accountable to someone, that there is someone above them, even if it's mostly in theory.
Instead of QMII we would have the Minister of Church as head of the State Church. I can't even remember the name or the face, or gender of that minister!
A fourth reason is that there is little political will to change the system. And even less public will. Not to mention that it will a huge trouble! Because it will require a change of the Constitution.
While an overhaul of the Constitution might be needed, it really doesn't matter that much. Because in most cases the Constitution de facto says that X, Y, Z is definite - unless another law says something else...
The Constitution is for most practical purposes not particular rigid.
So Frederik will in all likelihood become head of the State Church. Whether things will change before Christian sits on the throne is an open question, but it's far from certain, and not something that the DRF can plan for by not having Christian confirmed.