His job is less legitimate because he's sat around a table rather than on a building site?
They're a getting a mayor of Greater Manchester for their money. And the money isn't even a new spend, the mayor replaced the GM Police and Crime Commissioner post which also paid £100,000. It also replaces several other roles who presumably also had salaries attached to them.
Mayors set policy and strategy for local services. Every major city in the world has one, or sometimes several, people who do this. City mayors have existed for a couple of thousand years. Just like the Prime Minister sits at the head of the Cabinet, the Mayor is the head of the GMCA while the other council members are like the Cabinet.
Labour PR staff work in ministerial departments.
And an elected representative reacts to issues raised by the public who he represents and tries to do something about it? Well fuck me. Hang him. Obviously not doing his job in representing the public voice when he's .....errr..... representing the public voice.