Even without a tax in place (and I seriously and truly support putting a tax in place), millionaires and billionaires could take relatively small steps to improve life for a lot of people.
Do you remember last year that news story where a church used the donations from the collection plate to buy up the medical debt for some people? If I'm recalling correctly, the church bought up the debt, pennies on the dollar, and with like $50k were able to help over 100 people. I may have wrong figures for the money value and the number of people impacted, but I think the point remains that a lot of people's lives got better without the medical debt, both financially and emotionally.
Billionaires have the capacity to do this same type of thing. Just pick any city and throw money at a major problem that directly impacts citizens. You don't even need to work with the city or state government there! Get together with your other billionaire friends and strategize to pick a variety of cities. Make a game out of it about who can afford to pay off the problems in Los Angeles or Chicago, and who can only afford to pay off the problems in Sacramento or Springfield.