First, this is speculation but it makes sense given the existing incentive structure.
On its face, it would seem really obvious that a bank would want a short sale rather than a foreclosure.
This is because a bank incurs significant additional outlays when it becomes a landlord:
-trash outs
-key change
-attorneys
-repairs
-deed recordings
-tenant negotiations (usually a few thousand just in cash-for-keys)
In a short sale, all they do is approve a number and collect a check. If there is a junior lien or liens, the senior lien holder will authorize some paltry pay out to them (like $5000 on an $80000 second)
Generally a senior lien holder’s net is substantially higher in a short sale as compared to a foreclosure.
The monkey wrench here is greed.
Many times seconds will insist upon an unrealistic number or on a payment outside of escrow (which is illegal) or that they maintain the right to follow after the closing.
First lien holders (who are, as a rule, more cooperative) will sometimes insist on a large unsecured promissory note upon close (which basically amounts to a mortgage without a house) or will require that they retain the right to follow for the additional funds after close.
Recourse-heloc lenders will often follow on any short seller.
Outside of California, lenders follow borrowers (or sell the rights to follow) on almost every loan. Usually, the only out is bankruptcy (since people losing their houses don’t generally keep large holdings to pay on bad debts). Banks will often (though not always) not follow foreclosed upon people because it is assumed that walk-aways have no money and short sellers already are more motivated to make a debt as whole as possible.
Some states give protection to foreclosees that do not exist for short sellers.
In these cases, there is an institutional incentive that favors foreclosure.
And make no mistake, those added costs to the banks come out of taxpayers’ pockets.
Making a more sweeping rule like the one was suggesting would simplify this incentive structure dramatically.
It would turn it into a binary system:
Either you short sell and get more (as a settlement) or foreclose and get less (as a salvage). For junior liens it would be a choice between little (in a short payout) and nothing (when the senior lien forecloses and wipes out the junior lien’s interest).

I suspect this would wipe out a lot of bad debt really, really fast (and without the benefit of squatters and stolen appliances).

And then I would get to work on Mideast peace and world hunger and the ozone layer…