I'm pretty certain - that Jacos Reese Mog, Boris Johnson, Tristan Hunt, Nick Klegg, David Cameron, Michael Gove are neither noble crusaders nor people who have excelled in business. They are not 'top league' yet enjoy incredible positions of power - and increased wages is irrelevant to them.
They are to a man (and woman) privileged and entitled people to whom a career in politics is a right, and a career choice not an attempt to do some good or help people. The correlation between the percentage of those who have been to private schools and those in senior positions within government is so far out of kilter that it has to be by design and not by accident!
Consider again the tangible links between private schools (small percentage of the population) and Oxbridge (majority of places) and the links between Oxbridge and the government and also the City and Finance (high percentage) - the whole system is for the few not the many. This wouldn't end by closing down Oxbridge - they'd just make Exeter and London the new Oxbridge. It is fundamentally about privilege and entitlement. Increasing the pay for politicians isn't going to change that one iota - it will simple enable more Oxbridge types to enjoy politics and gain more influence.