So you would base aids to the less fortunate on the willingness of those who have more to "donate" to those who have less ?

How would you go to make it happen, practically ?

Since people willing to donate have no real vision of people who are in need, you would need some sort of organization to collect the donations and distribute them.

This organization would need to run some sort of policies in order to make sure the people asking for donations are actually in real need of those.

You also would need to pay the people needed to run these organizations, perform the checks, mantaining a database of people in need and donators, and perform the actual donations.

For any country (remember, a country is responsible to the welfare of all its citizens, not only the ones well-off), working with possibly millions of willing donors and petitioners, pulling off something like this without a predictable budget and some defined policies and rules is quite hard.

Thus the modern welfare state, which might not be an ideal (or even efficient) solution, but a better one has not been invented yet.