Charities don't give the money out equitably. For the most part they have an agenda and you either have to meet a criteria or do something for the charity. What happens to the people who don't meet the criteria or are incapable of what is asked? Gay youth make up something like 40% of the homeless children. I can guarantee you that most of the Christian charities would ask them to "renounce their wicked ways" before helping them. Since being gay isn't a choice, that would be a little difficult for the kids to do.
Charity isn't a guarantee. You say charity would be a more robust net and that may be true for some, but the net would definitely have larger holes in it than the one the government provides. A thin blanket is better than none at all.
I would also point out that terrible people always find a way. If we were to switch to social safety nets based on charity, there would immediately be people taking advantage of both sides of the system. The rich would use their promises of donations to distort the missions of charities to favor the rich and the scammers would set up shop finding ways of getting more than they should. That is inevitable.
In fact, while writing this, it occurred to me that shifting everything over to charity would allow for much less oversight. There would be more grift. What is the purpose of that? The charities that you know may be stellar, but you can't deny there are terrible people out there willing to use the word "charity" to make money. Heck, our president uses his "charity" to pay off his legal fees. It's like we are in a cave of scarcity and you anti-government people want the rest of us to throw away the flashlight. And it really sounds like you just don't want to pay taxes for the programs that you disagree with and to hell with other people.
Also, Medicare alone is 702 billion dollars per year. 402 billion isn't going to cover it.
Also, also, I realized that the system you are suggesting would resemble the scholarship system for colleges. Have you ever applied for scholarships? It is a PITA. It is always not enough, there are always conditions on the money, and you always find the great ones after it is too late to apply. Scholarships are what happen when you leave college tuition funding to charity.