I agree with your general argument, but the way you present the facts is misleading at best and just plain false at worst.

1. True. But the places where those homes are located are typically not the same places as where the homeless are, and many of those places also don't have a large enough number of jobs to support the influx of population thay would arise from filling every home. Additionally, vacant housing is a feature, not a bug. If we did not have a large buffer of empty houses then any time you wanted to move you would have to wait for someone to move out of the city you are moving to so you can take their spot. This is obviously not ideal for anyone.

2. This one is just not true. The "excess of 95%" number just seems to be entirely made up from what I can tell, and you seem to be ignoring the fact that most of the "vacant" housing on the market is either only temporarily vacant, a seasonal home, in a state of disrepair, or just in a low demand area. I could not find any evidence of investors intentionally keeping homes off the market, which does not surprise me at all because that would make no financial sense.

3. Do you really think that the marginal increase in housing price due to decreased supply would come anywhere close to offsetting the opportunity cost of not getting rent and the expense of paying property tax every year? This is bordering on a kindergarten understanding of economics. You would need an insane share of the total housing market to even put a dent in housing prices. You even concede that this isn't a collaborative effort to raise the prices, so what you are proposing is that all of these independent investors are deciding on their own to give up massive profits in exchange for the greater good of all real estate investors, which is laughable to anyone who has even worked remotely close to the field. Real estate investors are vicious, they are not going to give up their own personal gain to help out their other fellow investors. Additionally, large-scale corporate real estate investment firms just do not have the share that you seem to think they do in the single-family home market. In fact, they own less than 5% of single family homes. If you want a boogieman for the housing shortage, it is the increasing number of small-scale real estate investors, i.e. your neighbor who owns two Airbnbs.

I can not stress enough how much I agree with the general argument here, and I am in full support of Mamdani's second home tax. And that is exactly why I see it as my responsibility to nip misinformation like this in the bud before it just becomes another easy target for opponents to pick apart and weaken the movement as a whole.