I remember when London didn't have a mayor, London wasn't such a good city. There was no voice for London on the national stage or international stage. As a major world city and a major part of the UK economy it is ridiculous that we should not have a mayor and a team speaking up for the whole city.

The abolition of the GLC deliberately left a gap in political representation for Londoners with 32 competing boroughs without any coordination on transport, housing, pollution, etc. Those were the years when Edinburgh was the place to be for New Years Eve, there was almost no investment in commuter buses, trains, bikes, and there was remarkably little commercial or residential building compared to what the city has seen since 2004.
The people who are elected as mayor might not be to everybody's liking (that's the problem with a popularity contest / vote against the party of government).

As for climbing the greasy pole, I remember a previous candidate for London mayor going on to become PM and I've lost count of the number of unsuccessful candidates for London mayor to got appointed to the Lords (now there's a questionable use of public money).

I would also be amazed if you could get good senior executives for an organisation the size of TfL who would be paid less than £50k (less than a tube train driver).