The US might be a worse place for lower skilled jobs due to lack of public health and low minimum wage but at the other end of the spectrum most people would be giving up a lot of opportunities and income to move to countries like Australia or NZ. Our economies are comparatively small, undiversified and lacking investment.
As long as the US has wealthy safe haven states they are going to be a more attractive destination for people with high demand, high income jobs. As long as those safe havens and state rights exist I don’t think US citizens are going to qualify for entry as refugees for some time. In the unlikely event the law and society breaks down completely people will need to get in line with all the millions fleeing war and genocide. Those that get in through skilled immigration will need to carefully weigh up the significant financial and career consequences.