In italy not only you can lock it, you are allowed to change bank for lower rates (surroga) without any penalty

Also true in the US, the term of art here is "refinancing". Just about every homeowner I knew during Covid refinanced and now has a rock-bottom interest rate on their mortgage.

The downside of doing that is you end up "locked in" to the property too. They now have a strong disincentive to sell, because they'll lose that sweet sweet interest rate and relatively low payment. I'm unsure what the broader effect is on the market.