A new crop of politicians, who are not bought by unions, big business, etc., would make a difference.
The situation we have now is a result of politicians positioning themselves to amass more power. With that set of politicians entrenched in Washington, I do not think that any constitutional amendment will help—they will just ignore it, as they ignore the rest of the Constitution.
We don’t merely need new politicians—we need to keep them at home. Let them do their business by teleconference, but keep them at home where their constituents have easy access to them and can constantly remind them that they are not elected to increase their personal wealth and power, but to represent the people.
Your suggestion enhances the majoritarianism we have today. Our republic suffers from too much democracy, not too little.