As an US corporation they would still need FCC and FAA licenses for all launches. In addtion, operating in a country that is not a US ally will significantly complicate compliance with export control and ITAR. The main relief from regulation would be that EPA regulations don't apply, and that hasn't been a major holdup:
> In the Written Re-Evaluation, the FAA concluded that the issuance of a vehicle operator license for Starship/Super Heavy operations conforms to the prior environmental documentation, that the data contained in the 2022 Programmatic Environmental Assessment remains substantially valid, that there are no significant environmental changes, and all pertinent conditions and requirements of the prior approval have been met or will be met in the current action. Therefore, the preparation of a supplemental or new environmental document is not necessary to support the Proposed Action.
The biggest issue with their last launch was that the flight termination system failed to destroy the rocket in a prompt manner and needs to be re-certified, regardless of where they launch from.
> In the Written Re-Evaluation, the FAA concluded that the issuance of a vehicle operator license for Starship/Super Heavy operations conforms to the prior environmental documentation, that the data contained in the 2022 Programmatic Environmental Assessment remains substantially valid, that there are no significant environmental changes, and all pertinent conditions and requirements of the prior approval have been met or will be met in the current action. Therefore, the preparation of a supplemental or new environmental document is not necessary to support the Proposed Action.
The biggest issue with their last launch was that the flight termination system failed to destroy the rocket in a prompt manner and needs to be re-certified, regardless of where they launch from.