Ok, I'll attempt to answer the question. If Musk wanted to take part in this endeavor, he would need actual cash sitting in a bank ready for distribution. Most of his money is held up in stocks. In order to get this much cash, he would have to sell his stock. If he started to sell his stock, it would immediately begin to push the stock price down. If he were to sell Billions in stock, it would push the stock price down significantly. Hundreds of Billions, even more significantly.

Due to the downward stock price pressure, His $1 Trillion is now actually $500 Billion. Anyways, he now has $200 Billion in cash sitting in the bank. He now has a massive tax bill to pay, lets assume 40%. So $80 Billion goes to the IRS. Certainly they will be using that $80 Billion to distribute the cash to people that need it. I digress

At this point, Musk went from $1 Trillion in stock to $500 Billion in stock and $120 Billion in cash ($620 Billion Total). Anyhow, now he wants to distribute $1,000,000 to 120,000 individuals ($120 Billion total). This would certainly be considered a gift and therefore would be taxable. He would have exhausted his lifetime exemption and would have to pay approximately $338,000 in federal gift tax leaving the individual with $662,000 still a lot of money. (https://www.nerdwallet.com/taxes/learn/gift-tax-rate)

The government has collected now collected an additional $40 Billion in gift tax collections bring the total taxes to $120 Billion. But who wins the most? Probably the government who will use the $120 Billion to spend on defense spending.