Or alternatively we can just pay them a lot more since they'll make money anyway, disallow them from earning money in other ways and at least have their profits have no additional negative effects.

Not that I expect people would be comfortable paying politicians more (see how many complain about e.g. CEO pay) so I guess we are stuck with incentives for corruption instead.

I don't think we need to PAY them more to eliminate corruption - I think we need to change how campaigns are financed. Needing to raise millions every few years to keep your job makes you beholding to whoever has the money