It isn't that much more complicated than that — politics-wise, sure, but all you really need is housing and money to solve homelessness.
To get 20B$ in actual money to pay the above-mentioned contractors, you need to sell an additional 7.4B$ in shares (to pay the taxes). Selling 27B$ of your portfolio would inevitably mess with Amazon's stock price, the value of the company would tank and now your 20B$ endeavour effectively cost you 40B$ (remember he doesn't have 136B$ in currency in a vault).
Those homes that you are building needs to have clean water and will consume electricity, this is a maintenance cost that homeless people might not be able to afford so there is a yearly price to this endeavour unless you want to go back to square one. On top of that, the grid can't handle the surge that all these new homes require, you need to scale the producing capacity. This puts an additional strain on the global supply chain, again raising your prices.
Of course the above is just one big conjecture, but the point I am trying to get across is that it is never simple when these amounts of money are involved because other constraints will emerge that will limit what you can do with your seemingly unlimited amount of money.
There are 300M Americans. If 999/1,000 people say "hey, free housing is great, but I'm going to keep working" and 1/1,000 people say "hey, free housing! I can just kick back", we now have an extra 300,000 people who are on the dole (almost DOUBLE the current number of homeless).
It's still only one step above complete destitution. Most people would prefer better and would still work hard.
It's a lot easier for a person to get a job, or beat any personal issues they have if they have a stable, safe roof over their heads. You gotta give people boots so they have bootstraps to pull themselves up by.
If you can afford to keep people afloat, you should do it. The less complicated and less strings attached the more effective and cheaper is your solution.
There are people who steer the discussion to those who stay dependent. They claim that some of those are "incentivized" to do so, in other words: they are lazy and greedy. Well that's true, and it's a problem. Primarily because they can be used as an excuse and as a scapegoat to distract from the fact that capital _owners_ are extracting power and value that is generated by workers and small businesses.
What would I do if I were in that position? Be Jeff? I don't know, I'd probably be just as full of myself to believe that I deserve to be treated like a monarch and be able to buy what ever I want, while cheating my business partners, exploiting and surveilling my workers, manipulating my customers and ignoring my responsibilities as a citizen.
Power should be somewhat proportional with responsibility. I'm pretty sure it isn't, not at that scale.