It is certainly stated somewhere in the fine print that the LV must be serviced. Otherwise, the bank would be taking on a much too high risk regarding the collateral.
The premium exemption is a right arising from the insurance. Usually, the assignee receives all rights and claims from the assigned life insurance within the scope of usual security agreements. Thus, this also includes the right to premium exemption.
However, it remains questionable on what grounds the bank should reject the application for premium exemption. Especially since the ability to service the debt is rather reduced by the (unnecessary) premium of the life insurance. There is also an obligation to release (even partially) in case of over-collateralization. By the way, even if the bank does not like it.
If the bank were to keep both insurances and finally reject the premium exemption as a secondary solution, in my opinion, this would be acting in bad faith.
But: This does not have to happen if one speaks reasonably with the responsible persons at the bank and does not just have a phone call with (some) clerk who (apparently) took the answer a bit too easy.
Now I want to add my two cents as well.
The reason why the bank rejects the early repayment can only be speculated here. We don't know the contract in detail.
However, in my view, a premium exemption of the insurances should be possible. The bank's consent is certainly required for this (e.g., the insurance is not yet valuable enough - in that case, a premium exemption would endanger the collateral).
Here (with sufficiently high collateral), however, I see no reason to refuse the premium exemption.
You should – as already recommended – contact your "regular" advisor for this. He knows you, can assess your circumstances, and also sees that you want to act before the horse has bolted. Such things are difficult over the phone. What is said gets lost during the conversation, other possibilities are not considered, and the employee on the other end of the line may still have a whole bunch of work on his desk. For him, you may be an unknown case among many that should be handled quickly.
However: Could it be that the loan was taken out via an online bank? Or why are you trying to clarify such things in the impersonal, telephonic way?