The rockstar's locally inflated salary goes down of course.
That means when remote work is a norm salary shouldn't go down when the employee moved to Sydney from SF.
Unfortunately, that’s not how payroll taxes work. You absolutely need to provide your employer with your real address. If you move out of state (or out of the country) there are very real tax liability issues that they will need to address. If you work for a decent company, they may even help you address your personal tax liabilities too.