It is interesting that banks dont already offer this for a fee. Im not too knowledgeable on the topic, but wonder if it has do with how mortgages are bundled, and the cost/paperwork of unwinding that.
However, this upside should be priced into the Mortgage price on the secondary market as well.
there are other factors as well, like holders of mortgages may care about much more than their market value. They are balancing time returns, risks, and their portfolio of investments.
The point of the Danish system is that it's a market system through and through. No one needs to twist the arms of lenders to make them "allow" something.
The value calculation might have to change, as noted by fshbbdssbbgdd, but it's possible, since the Danish system calculates a value on the bonds that represent the mortgage. To me it seems like less overhead to forego the step of issuing the bonds and just make the mortgage work like the bonds would.
I believe the difference is that mortgages are tied to the individual property, and thus individually priced, whereas building bonds are part of an emission series. That means there's a liquid market, where all you have to do to pay back the loan is buy your bond type, not the particular bond for your property.
And that makes it different from a mortgage that is a contract between a single lender and a single borrower. There, you are stuck doing business with whomever owns the contract, and they can use that against you when negotiating the price.