"The problem is a lack of transparency" might have been true in some historical era when there was less money involved; We could target a singular corrupt politician taking bribes if we knew about the bribes. Sure.
But that's not the problem we have. Our problem is fund-raising. Politicians are not meeting once every few years with a lobbyist at 2AM beneath the Lincoln Memorial, they're spending 60% of their time on the phone begging moneyed interests for reelection campaign funds or party goals, the day after they get elected. They're spending 25% of their time negotiating with lobbyists about what laws the lobbyists get to write ("The legislative subsidy model" of RL Hall, wherein they replace Congressional staff increases), and another 10% trying to raise their professional profile through non-legislative activities in the press or with political powerbrokers. Maybe 5% of their time is spent in committee meetings or on the floor.
On top of that, it starts out as a part-time job, with meaningful meetings limited to a few days of the week in order to satisfy the need to fly home to meet with contributors. The Senate has become nearly impossible to get bills through for a similar reason - a filibuster is a time-wasting annoyance legislatively, but its requirement that 51 Senators stay on the floor to break it prevents them from spending days fundraising, an existential threat to their careers, while the filibustering party only has to commit a couple Senators to keep it active.
Of the bills voted on in their legislative career, the proportion actually read by the legislator will be under 1%. The number read in full by their staff, under 10%.
Politicans are not hiding this; They are complaining about it. We have created a system wherein legislating ranks as the lowest priority, and not even the wealthiest in Congress can be free of implicit corruption.