Then there are ongoing regulations like needing to have a resident director, so if you're a single-director company you can't move your personal residence even to another European country without shutting down your business and re-establishing it in your new country.
Running it also changes from country to country, so if you move you have to speak to new accounts and lawyers in your new country about how tax and vat and other legalities work.
In theory, this would let you do all of that once, hopefully all online and in a simpler and faster way. Then it should also be easier to hire and sell to all EU countries without doing a complicated dance of employment regulations and VAT compliance.
That would be ideal anyway. Not sure if or when we'll get there.