The counter to that is that you are making the problem grater by taking the responsibility of peoples actions away in the first place. The argument that you are making here relies on the premise that the state and society is guaranteed to be paying for these instances in the first place.
IMHO, not taking that responsibility in the first place is the 'financially should' decision though that is not the only consideration here. When removing the responsibility of your actions you are simply ensuring that MORE irresponsible behavior is going to take place.
The problem with doing it your way is, there are children who are helped by welfare who would otherwise suffer through no fault of their own because our system prefers to financially assist parents rather than remove kids for neglect whenever possible.
My way?
I did not actually present a solution. I was pointing out the fatal flaw in the premise of the post that I quoted. The entire argument that was made relied on the premise that the actions of government did NOT influence behavior. That is flat out incorrect. By supporting those that make poor decisions, you create more poor decisions.
I agree with some of the solutions presented in this thread like removing money from the equation altogether like actually doling out food instead of food stamps. I like the way that WIC is run. You get a check but instead of X dollars on your check there is 1lb cheese, 1 box of cereal ect. You can ONLY purchase the foods that are on that list.
Essentially, I believe in welfare being a helping hand for those that need it but NOT something that is meant to make your life comfortable while using it. People should get help that is needed and then get off of it. That would happen if welfare programs were not structured in a way that makes it preferable to actually working.