This is a horrible idea in practice because everything that is public and open turns into a purity test.
You need people to be able to negotiate with each other in order for consensus to be established, and negotiations only work if the negotiators give up on something that they want to get something else. The moment you make this public all that you get is people turning negotiations into a way to generate soundbites and scared of doing any actual work because they'll just give ammunition to their opponents.
This is doubly bad in the US with the primary systems which makes legislators even more vulnerable to attacks from their flanks.
Legislators are not elected to be proxies for the voters, that's not how it's supposed to work. They're elected to use their judgement, that's why there usually aren't recall elections or restrictions on how they can vote etc.
As a matter of fact I'm of the opinion politics everywhere would be a lot better if plenaries, committees and hearings were not recorded or televised in the first place. I'm ok with minutes being made available but I'm convinced without being able to clip soundbites or tiktoks out of every meeting legislatures would be a lot more productive. Definitely more so than if we attached a camera crew to everyone in politics for "transparency"