Ironically, the largest beneficiaries of the mortgage interest deduction are the banks. If you give one person a subsidy, it allows that person to buy a home when they otherwise couldn't. If you give everyone a subsidy, they just bid up housing prices by nearly the entire amount of the subsidy. (If the government really wanted to make it easier to own a home, they should subsidize new home construction in order to increase the supply of homes and thereby reduce their cost.)

But once you've established the deduction and people have already bought homes expecting it, they require its continued existence to be able to keep making the payments.

What they really ought to do is remove the deduction for new mortgages but not existing mortgages (or refinances of existing mortgages that don't increase the loan principal).