It's innocent until proven guilty, not innocent until investigated.
But yes, it would be politicized immediately. If only there was a way to have bad faith actors run a government smoothly, then we'd be cooking with gas.
Getting the money out of elections would go a long way. The problem is that more than half the ones who need to choose to get the money out benefit from it.
The same FBI that was dismissed by Trump when they looked into him, even though he was totally guilty? Or the same FBI that told civil rights protestors to kill themselves?
The FBI is the Federal police for crimes the common man commits, not the rich.