Unemployment benefits are insurance payouts (at least for the first 26 weeks) which are ultimately paid for by workers - in the form of lower wages.
I have no problem with someone collecting their paid-for benefits, and moving somewhere else where the cost of living is cheaper. In fact many of the State UI systems encourage recipients to move out-of-state "where the jobs are". Presumably they become somebody else's problem.
I can match your story of a feckless 20-something with stories of over two dozen "40-somethings" who are still trying to support their families on what is left of their savings. A (very)few of them have managed to find jobs, and the UI payments are what allowed them to stretch out their savings long enough to do so.
The UI system is effective at keeping formerly middle-class workers away from destitution for long enough to find some kind of job.
If you are looking for something to cut, try the Ethanol subsidies and the "mandate" to include 10% ethanol at the pump. Lower fuel costs would help almost everybody and some business might even pick up enough to start hiring again.
How long do you think unemployment benefits should last? Forever?