Lobbying is not the same as decision making power, most corporations have dedicated lobbyists, it's influence perhaps, but that is a fault of the political system itself, not the monarchy.

Veto has limited power, politicians simply amend the bill, so time consuming but not much else. It's also not used that often.

Establishing inquiries is also not really power to govern, it's reporting on those who do.

The monarchy going on royal visits or tours is not political, it's keeping up appearances.

They have no real power of governance.