Everyone who had less than $100k would be richer.
In the limit you could give everyone a trillion dollars, and we'd all be equal.
This is a thought experiment. My point is that wealth is real and meaningful and can be adjusted.
In the medium term, you have to ask yourself who is able to capture this money. Not for sure the homeless that has no means to start with. Probably will be captured by the people that control directly or indirectly the manufacturing means. So the rich will be the one capturing most of the helicopter money.
The reason is that money is not capital. Money by itself does not produce value. One of the most effective ways to increase social mobility is by investing in education because allows people to acquire social capital that they could invest to generate real capital and then money.
Bill Gates doesn't live in a $40B house.
After he gets a million dollars he will have money to buy a $30 loaf of bread.
Actually, I guess, the real losers would be middle class...
But the truth is: money is just a tool, a way to get something.
In your example, there's no point in giving a million dollars to the homeless, it would make much more sense to make the $3 loaf cost 0,3 cents. Now everybody can buy it.
But if you just drop money in the lap of somebody that doesn't know how to produce value and change this value for money, those who produce the real value and owns the means to produce it will still making more money from those who can't produce.
To solve that: take the homeless, provide basic care and opportunities for him start to produce value. Then the money will come.
The world doesn't need most of the people to work. Today what you actually consume is produced by <20% of people working. Most products are produced by machines and not labor.
The homeless don't need to work, because society can provide for them even if they don't.