Individual responsibility would do just the opposite. But no matter what imprudent people do, their behavior is no reason to infringe upon the freedom of everyone else. Just because some people might fail to take adequate precautions against the possibility of unemployment is no justification for forcing everyone to participate in a coercive, inequitable and wasteful system. We have put up with the government's collectivistic UI system for more than sixty years. That is long enough for it to have become something of a sacred cow.
Most people unthinkingly accept it and have never considered any alternative.
The notion that unemployment compensation must be a function of the government is deeply ingrained. But it is mistaken. Individuals can and should make their own preparations for periods of unemployment and they can do so better than government. The entire UI system should be repealed. Any step short of that is inconsistent with the ideal of human liberty.