Much of this can be achieved by modification of the rules for the Senate or the House, and a majority could do it. Currently, it’s easy for lobbyists to sneak their provisions into bills in the dead of night, and everyone plays dumb as to how that provision got into the bill. If every modification to a proposed piece of legislation is treated like a checkin, with full history preserved at each stage, you’d have a name attached to every revision and there would be nowhere to hide.
The people who would lose most if we did this typically call themselves “centrists”. They have no strong ideology beyond keeping the donors happy.