How about charging them for their public costs? If you get rescued by helicopter because you went skiing out of bounds at a resort and got lost, don't they send you a bill? How about that for people with money who abuse the system while abusing other things?
All economics are redistribution, it's simply the details that change with the methods. It is unrealistic to want a world where each person pays exactly for what they consume or are liable for.
Maybe you are right but I cannot understand or agree with this idea that has taken hold among some on the internet that we should be happy to pay taxes because the government will go and solve problems with that money. Beyond the fact that the government is horrible at allocating resources and using them efficiently, every tax is a dollar being taken from the economy that could have gone to people that produce things of value not what some bureaucrat decided was of value.
Sending the bill to the family is dumb but there's sense in sending the person responsible for damages bills. I think we already mostly do that though, they just don't always pay the bill.
Keep that ASBO trash on the other side of the pond.