People don't have the right to live wherever they want but in the United States the government(local or federal) should not be able to limit immigration of citi

People don't have the right to live wherever they want but in the United States the government(local or federal) should not be able to limit immigration of citizens between regions inside the country. I fail to see the difference between visa requirements for foreigners that wish to live in the United States and a rent requirement to live in the Bay Area. Obviously San Francisco and the Bay Area are not sovereign so they can't require visas and border control but they have instituted a system that has the same effect. Notice that I assume government regulations are the sole cause of high housing costs in the Bay Area. Another question worth asking would be how stringent do your housing regulations have to be to be considered a violation of other citizens' freedoms?