You're right. I hadn't considered that it's such a boon to lenders. Tax (or deduction) incidence is an interesting rabbit hole. It almost makes tax law really interesting. There's a thought piece that I come back to often. It's an episode on Planet Money called The No-Brainer Economic Platform. In it, six economists that span the political spectrum present six policy changes they'd make to the economy. Importantly, it's six policy ideas they all agree on. And first on that list? The MID. But the other ideas are great, too. It's revealing that all of them are political non-starters.
You're missing the fundamental problem: no one can afford their houses. And they all know it. Not only that, but the MID is really only useful to those who can afford their houses otherwise. Did you itemize? Did I? Do you know anyone who did? For everyone who is actually strapped by paying for their house, the MID is a fantasy. For everyone who is reallocating this that or the other in order to sustain their lifestyle, the MID is a factor.