I don't understand your confusion. If they want to keep their tax benefit, they pay for it by having reduced labor mobility. If they are okay with giving up their tax benefit, they get their labor mobility back.

Why should they have both, at the expense of others?

That's a bait and switch. Perhaps they wouldn't have made the purchase without the incentive. If the mortgage goes underwater because the law is changed, then they lose a lot more than a tax benefit.

I think you're missing out the core conceit of this thread: ENDING the mortgage deduction hits all current house owners, and drives down prices for all currently owned houses.