This is only because the drafters of the US constitution didn’t think to list corporations law as an enumerated power of Congress - I don’t think they omitted it out of an ideological conviction, simply because nobody thought of it at the time. That said, given SCOTUS’ expansive reading of the interstate commerce clause, there’s a decent chance SCOTUS would let them get away with a federal corporations law, but they’ve never had the political will to attempt a general federal incorporation law
The drafters of the Australian constitution did list corporations law as a power of the federal government-but they were working over a century later, and they studied the US system intently to try to identify what worked and what mistakes to avoid. However, it took until 1989 for a federal corporations law to be enacted, and then the High Court ruled in 1990 that the new federal corporations law was unconstitutional, because the corporations power in the constitution only authorised federal regulation of existing domestic corporations, not the act of incorporating them - however, this was fixed by a federal-state agreement voluntarily ceding corporations law power to the Commonwealth (this is another innovation the Australian constitution has compared to the US - the ability of the federal level to gain new enumerated powers without constitutional amendment, by the states voluntarily agreeing to cede them)
It’s possible to be registered in a state you’ve never been to - how many people have actually been to Delaware or Wyoming - and employ nobody at.
Some countries play this game too - after the Cayman Islands enacted anti money laundering laws, they tried to keep companies with privacy and efficient dispute resolution.
Anyway, I don't know about the exact wiring of this but an alternative can be to create a virtual country with its own law, sign a trade agreement with the country to give it full access to the EU market and even some special rights and achieve the same effect of getting rid of the regulations and bureaucracy. These arrangements can be very interesting, like the City of London which is like a country inside London that is actually a corporation. Very weird things are possible.
That means there’s no barrier to movement.
It’d also possible to reincorporate relatively easily.