Except it does not work that way in the US, you can freely incorporate in any state without worrying about this kind of tax drama. The EU really needs to improve the integration of their single market, as this is precisely the kind of barrier preventing people from exploring what other EU states have to offer.

It does here, at least in California. eg if you live in CA and own a DE llc, that llc will have income apportioned to CA.

Not quiet. Your profits from the business will just get taxed as a CA resident to your personally.

If an LLC does activity in California, it's subject to income apportionment in CA.