Here is my alternative approach (with the actual approach being to abolish it).
If we must have a Welfare State, then lets have a welfare State. Lets declare a specific state to be the only place where one could live to collect welfare for a period of longer than one year. And not just have a mailbox there. Actually reside there for 10 months out of the year. All the businesses and doctors and non-welfare-collectors that wanted to move there could move there. Then we could still have a welfare state, but without the problems being spread out amongst the working.