"the public" tend to not have much cash on hand, especially in times of crisis. Those that would have benefitted from a massive real estate firesale would have been savvy 0.1 percenters.
That’s not true at all. I worked at one of the big pe firms that made lots of money from 2008. Their goal was to move things to profitability asap. Either get a loan to performing (via getting holder to repay or rent), sell the note, or foreclose and sell the property (sometimes to a sister company). Same goes for anyone holding a property. Empty properties are targets for squatting and quickly fall into disrepair. The last thing a savvy investor wants is a nonperforming property.
...and a massive plunge in real estate values would probably cause a lot of existing property owners to be upside-down on their holdings, forcing many to sell and/or default on their mortgage/debt repayments, which is sort of how this got started in the first place
On the monetary side it's hard to say which would have been better. There were people in debt, so keeping deflation at bay was important. Then again, even if 0.1 percenters bought these, overall cost of living and consumables would be cheaper, and debt is generally dischargeable, so you could argue keeping deflation at bay wasn't really to protect the debtors but the debt holders.
All said, well considered fiscal stimulus years ago would have been most directly beneficial to "the public" among all measures.
If a good chunk of the population is doing it it becomes less stressful. It's not like the alternate route (the one we took) has been stress free either.