I work in risk management at a bank and I dont think any bank will incentivize you to pay back a loan early. We certainly would not. Prepayment (risk) is only an issue if rates decline and people refinance at a lower rate. The current situation is no concern if the interest rate risk was managed properly by the bank.
There are numerous ways to get rid of interest rate risk if you have lots of fixed rate loans on your book. You can repackage and sell the mortgages to take them of your book (which means someone else at least has to deal with hedging it now). You can issue covered bonds at a fixed rate as well, which means your rate add stays constant throughout the entire period. You can enter Fixed-Float interest rate swaps, to get rid of the fixed rate. Also, central banks across the spectrum flooded banks with liquidty. The ECB created so called Targeted Long Term Refinancing Operations TLTROs where banks just sat on excess liquidity anyways. Your loan can (at least in many cases) be used as collateral or in securitization when borrowing money from a central bank or getting reverse repos from Eurex etc. It is an asset for the bank, not a liability. Having assets is almost always desirable...
Flipping it around, I would thin twice about paying back a fixed rate loan now. As long as inflation is high, and your income increases alongside, sitting on a long term low fixed rate loan is quite a good thing to have.
Lastly, there are lots of variable rate loans anyways (people love the lower initial rate). This is also easy to check because most regulations require banks to provide this data to the respective national competent authority (NCA).
Some EURO area data can be found here.
The original data, with newer values, should be found here.
In the US, you can look at the Mortgage Bankers Association. Ironically, the share of ARMs (adjustable rate mortgages) increased to 11 percent of overall loans and to 19 percent by dollar volume, as more borrowers continue to utilize ARMs to combat higher rates. You can also read about this on Bloomberg. As you can see, despite rising rates, there are actually more Americans willing to take out ARMs than before, mainly because a variable rate will (almost) always be cheaper to a fixed rate mortgage when you enter it.
In contrast, UK mortgage borrowers seem to be more cautious, as can be seen in chart 2 of this link.
However, it is worth noting that UK mortgages frequently have a fixed term fixed rate that is shorter than the entire mortgage period, meaning in the medium run this can change for existing mortgages as well. The original data can be found here.
