Has anyone done an EA-style analysis of US campaign finance reform?

Earlier this year, the House passed a bill (HR 1) that seemed promising. It quickly got blocked in the Senate, where it has 47 Democratic votes but seems like McConnell is keeping Republicans aligned against it.

Lawrence Lessig gestures to why campaign finance reform is leveraged on Joe Rogan (around 21:30):

Now, almost everybody realizes that until we fix this broken Congress, nothing else can happen.

So it's not like this is the most important issue out there – you can think of climate change or healthcare or jobs or competitive markets – you can think of those as the important issues.

But what people are increasingly seeing is that this is the first issue. If we don't fix this, we don't fix anything.

Given that HR 1 got through the House, could be tractable. Definitely impactful.

You could imagine convincing 4 Republican senators that their funding needs would be fully met for let's say the next 4 races they pass good campaign finance reform (perhaps HR 1 v2). This could push it through the Senate for a total spend of ~$200m (4 senators * 4 elections * $12m/election).

Not cheap, but probably a good buy for the impact this would have if done well: campaign finance reform => more functional & representative US federal govt => sensible policy work can be done federally in basically every area we care about.

(Not sure if Trump would veto, perhaps better to do this once he's out of office.)

Could imagine getting Lawrence Lessig to architect it; I bet he'd be down.

I haven't thought about this super closely and it's definitely complicated territory, but I haven't run into anything that immediately disqualifies it.

Has anyone poked into this more thoroughly?

Looks like Open Phil thought a bit about it in 2013 (1, 2) and came away somewhat bearish, but that was just a quick look & was well before things thawed (i.e. before Pelosi was getting comprehensive campaign finance reform through the House).