Lobbying occurs because the government has power. It's that simple. Power corrupts, and absolute power corrupts absolutely.
Politicians want to be politicians because the government has power, and that power gives them the ability to (legally, by the way) dole out things that benefit the entities that helped them get elected. Term limits, low pay, no benefits, etc. does not really remove that incentive. You'd clean out the sludge once every few years, but it is refilled with people who want to come in right after them. Most DC politicians are independently wealthy before they come to Congress anyway. Bob Corker, for example, is not there because the Senate has a great benefits package.
In a relationship between a bribe-maker and a bribe-taker, the bribe-taker has the power. If you want to help solve the problem, you have to take away the thing that bribe-taker intends to give in exchange for the bribe.