The subsidy is enormous compared to the cost of other housing programs, and it almost all goes to well-off or rich people. So, no, your TLDR is not accurate, as it points to homeownership as an important wealth-building mechasism for those who can afford it. Furthermore, since the FHA was straight-up refusing to insure mortgages in black communities until 19-freaking-68, there is a strong historical effect of perpetuating racial inequalities by making only whites eligible for housing subsidies. We spend more than four times as much on mortgage interest than Section 8 housing subsidies.

TL;DR: The mortgage interest deduction is a welfare payment that you have to be rich (and until 1968, white) to get. Maybe we shouldn't spend $71 billion a year on it.