Your hypothesis assumes that all elected officials must engage in some form of bribery or pay for play. In an ideal world we’d find leaders who put the interests of the country ahead of their finances.
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
