I don't read the GP as asking for centralization.
I think there are multiple approaches that can be made to make it less of an issue:
1. Split the presidency into a triumvirate, with elections every two years for the oldest serving member (like the Senate) - this way you reduce the power of those elected, making it easier to get rid of them in the event of a corruption scandal. Right now, for understandable reasons, the President is considered above the law because of the sheer logistics of having the country have unbroken governance in the event of an arrest. I'm not suggesting members of the triumvirate should be arrestable for unpaid parking tickets, but making it easier for Congress to deal with corruption without feeling there'd be a "constitutional crisis" or that they'd lose a figurehead they've based their entire identity around if they did would be a massive improvement.
(As an aside, a triumvirate would reduce the attraction of the presidency for those not interested in public service.)
2. Create an absolute code of ethics. Have Congress mandate the IRS release tax returns of all candidates for Federal elected office. Require all elected officials place their estates in the hands of independent groups for while they're in office. (Don't like it? Don't run for f---ing office! You're supposed to be making the people rich, not yourself.) Make this a requirement before anyone is even presented to them as "elected to office" - ie if you don't do it the date you'd normally be sworn in, you're treated as someone who already resigned from office.
3. Give all elected officials a salary that's high enough to sustain a comfortable DC residence and a local residence, and an expenses system that allows them to travel, have a reasonable level of staffing, and so on, so they have zero need for outside income for anything other than campaigning. The fewer excuses an elected official can have for receiving and spending money, the easier it is to catch them when they're caught.
These three changes would be unpopular in some quarters, but I've yet to hear a coherent argument as to why an investor who plans to continue running investment companies for another 40 years is somehow a better politician than a community organizer.