In non-recourse states, you'd expect to see defaults as people leave the keys in the mail to reduce their housing costs by moving next door at the reduced price or rent. More broadly, people don't like seeing their wealth go down.
> Is a tax dollar better spent placating grumpy homeowners
If it gets you the reform, yes. The point is you don't get housing reform with grumpy homeowners barring a massive shift in voting patterns.
Also, let's keep scope in mind. You only need to bail anyout out if you reduce home prices. If you hold them constant in nominal terms, that shouldn't generate pushback. (If you hold them constant in real terms, people can continue feeling wealthier.)