It sounds like a great idea. It doesn t even have to be an entire state. They could "free economic zones" or something like that where people can get permits to live and work. This would be great for startups who have investors, founders, and employees around the world. A Si Valley company, Blueseed, already tried unsuccessfully to do this on a re-purposed cruise ship.
The problems I see are Constitutional. The Constitution ensures free travel within the US. But to make this system work, we d need some sort of checkpoints on people leaving the free zones. Also, the free zones would want to set up their own immigration rules to allow in a limited number of people, with certain skills, and with a lack of violent criminal record.
If they could get through the Constitutional issues, I would support the idea.