We currently have a system of public financing for presidential candidates. Many other countries, and even some states within the US, go even further. They finance the campaigns of all candidates for their legislatures. It would certainly decrease both the appearance and reality of interest group influence. The downside, however, is that you have to pay for it.
Public funding costs money.
Ultimately, only you can decide if such as system is needed for other elected offices in the United States, or if some other reforms will do the trick. You can use some of the following links to help you decide. Comment on the Question of the Week or anything else that's on your mind.