Forget mortgage interest deductions. Take a look at cash back rewards cards. Cash-using households ultimately end up transferring money to card-using households this way, because merchants don't usually set higher prices for card users to compensate for fees. See https://www.bostonfed.org/publications/public-policy-discuss...
I get an average of 1-2% off of almost everything I buy simply because I can use a cash back rewards card to do it. It's sickening.
Is there something stopping poor people from getting these cards? I mean sure, if they have bad credit they can't, but I know plenty of poor people with good credit.
Compare the sheer toil of using food stamps vs using the mortgage tax deduction.