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Hmm, I got curious and asked AI about this. I actually started with something simpler than what you proposed:
"Are there mortgages where I can keep the terms of the loan while moving to a new house? There seem to be gains from trade to be had with the existing investor (I pay a slightly higher rate, though still not market rate; they let me switch the underlying collateral)."
Claude told me that what I'm describing is a portable mortgage, which does not exist in the US but does in Canada and the UK.
Claude told me that some mortgages in the US are assumable mortgages, which means that a new buyer can assume the terms of your loan when you sell it to them.
Neither is quite what you described, but have a similar flavor of reducing mortgage lock-in.
It sounds like two people with assumable mortgages could basically execute a swap.
Yeah, the problem is that the deal is with a particular borrower and there's a good chance one of the banks would prefer their current borrower to the new one.
Obviously, we could just move into each others' homes and do an informal swap, but that creates the same kind of incentive problem as renting.