There is only one answer which I don't see in the replies to this comment (weird).
Burning Steem decreases the supply, which is the number of coins on the market. As the market cap of steem does not change, this means that the price of steem goes up.
You want to give money to everyone, well, the price going up does exactly that, it gives money to all steem holders. However, creating new steem and distributing it to everyone equally will not really give money to people because the price will move down (since again the market cap doesn't change).
The market cap is the value of all the steem coins together.
So, when you see burning, it means that everyone holding steem is benefitting from it equally.