In part, capturing of interests comes from a politician becoming old. Bernie is an exception, but most aging politicians get used to their 'nest' and being set in their ways. This is bad, as it prevents new young blood being consistently introduced into the system to represent the younger half of the population. What we lose in experience, we replace with the conviction and audacity of youth.
Ideally, the older departed politicians would spend time on mentoring people during their retirement if politics is what motivates them.
As to the concept of pay that you outlined, I don't disagree. I think that part of a overhaul for a reworked America is UBI, alongside income, wealth, and asset caps. Part of it is that leadership in organizations should have their pay grade set by workers within the organization - the CEO needs the rank and file workers to decide whether they keep the CEO, and if so, where to set the pay bracket. In turn, this could also apply to politicians. Initially they start at a waitress's* pay in office, and then voters can vote on the politician's income every year or so. The trading of favors would remain an issue, though the implementation that I have in mind would make it easier to track corruption. It is harder to own more than one yacht, when that costs more than the asset cap that affords a good house and car.
*If a politician can't live on a waiter's income, then that income ain't fit for a human. Having the initial income of a politician reflect society at large would help make them reflect on the economy and its effect on people.