People that really feel this responsibility become foster parents. But saying the state should deal with them isn't taking on that responsibility - at the end of the day actual people need to be their parents. I'm happy to support those people by having taxes directed their way, but the state doesn't get credit for their good deeds.
The common US system where foster families receive funds to provide temporary care for kids in the system isn’t parenting it’s a disaster that’s a massive disservice to kids in the system. In many individual cases it works, but overall it also results in unacceptable amounts of mental, physical, and sometimes even sexual abuse.
Your statement reeks of someone who lives in an ivory tower somewhere.
Put another way, when we don't rely on governments to help with things like this - does that incentivize people to take on responsibility? I suspect not...