That's not the only solution I think we should be implementing, though. We could subsidize housing for people that can't afford it in other ways - giving people money to pay for their apartment through social programs after considering their income, rent, and expenses to get a grip on their actual ability to pay for available housing. All without having a hard-line income cutoff for this stuff (which doesn't help when the numbers are out of balance with the local situation). Building housing will hopefully help folks so long as there is a shortage, but it isn't a cure-all either.
Folks aren't generally getting rich from HUD: In Indiana, at least, lots won't accept HUD due to regulations and not paying on time. The last bit should be fixed, the first bit should just be standard for rentals. Landlords wouldn't necessarily know if they just let it be shown as regular income.
Besides, this does hinge on there being enough housing - including a few empty places. It is better to generally have empty units available just like you want a little unemployment to have a pool of employees to choose from.
Education is not housing, though, and has different goals. Education subsidies at higher levels is off. If we just paid most of the tuition and books, I think folks would care more that the schools are spending on sports instead of education. I'd certainly not do it with tax dollars and not allow colleges to charge students. Sports scholarships would be a thing of the past. I also think we could revamp degrees to have more pointed classes, insisting the "well rounded" education happen before college. It could probably actually make a masters be a 5 and sometimes 6 year program instead of 6-7 years, for example.
At the lower levels, some of our problem is funding by school district instead of distributing state-wide or country-wide. School are still segregated in many ways and the system has created wide disparities between schools because of funding. Sure, you need to adapt a little to the local level, but that's mostly for things like more special education students, more students not speaking english, and/or higher rates of poverty, which affects learning. The last case is some of what has made some of our schools bad, and the rest of us act like we don't care because it isn't our kids.
How and who would you tax? Someone that just lost their house to the bank, for example... does the bank pay? The person that got sick and lost their job and home? Only empty rental units?
There is a little merit for the last one, so long as it is reasonable. You want some empty units on the market in most price ranges at all times, just like it is good to have some unemployment so folks can replace workers and have a pool to choose from. You don't really want rental units to sit empty for 6 to 12 months, though, and is probably a sign that there are many short-term rentals or the landlord is charging too much. Even this only works if the landlord can prove he's being prudent with pricing - a simple mortgage + average upkeep + fair set profit percentage would do, so long as it isn't obviously in the landlords favor.
If someone lost their house to the bank, the bank would be liable while they control the house. Main focus is on empty rental units or empty investment properties.
Presumably you'd need some window of exemption for normal transfers and typical moving times.
I'd probably implement as ~2x property tax on dwellings unoccupied for more than 3 months in the past calendar year. As you pointed out, this would have a downward pressure on rents, as landlords would be less able to leave an apartment empty while they wait for someone willing to pay the highest rate. Also, people who own multiple houses would be penalized for keeping some of those houses empty without renting them out.
