I have no desire to take their private - note private - wealth away from them. They are welcome to it, as long as they pay tax on the same basis as any other citizen.
What mayors do you object to?
The ceremonial mayors, like the Lord Mayor of Manchester? All they do is cut ribbons, and attend flower shows and the like. They have no executive power. They are purely decorative and ceremonial.
Executive mayors like Andy Burnham? If you didn't have them, someone else would have to do their job. That someone else would almost certainly not be directed elected. Favourite would be the Chair, for the time being, of the Greater Manchester Combined Authority. I fail to see how that would be more democratic or more efficient. It would be like replacing the PM with the Chair of the Parliamentary Public Accounts Committee.
I find it odd that some people are opposed to devolution. Do you prefer decisions to be taken by some faceless bureaucrat in Whitehall, who has never been north of Oxford and doesn't know Hulme from Halifax? Because generally people dislike and distrust the Sir Humphreys of Whitehall.
As I said, if you get rid of Burnham, someone else has to do the job. Someone else has to make the decisions. Contrary to the perceived image, Burnham is not some czar with absolute powers. He has to get the GMCA representatives to go along with him, and he has to stay within the law. He, and the GMCA representatives, are all elected by the people of Greater Manchester.