The lack of coordination tooling isn't the problem, the complex interlocking structure of conflicting interests is. The obvious fallout of a congressional communication tool is that it becomes a firehouse of what congress members strategically share to further their own goals.

Part of the problem is probably that there is no money in it: Congressional offices don't have a big enough budget for the staff they need, much less any pieces of software/services.

Isn't software a tool for leverage? If staff is additive, then software is multiplicative. The right software would allow a staff of 10 to do the work of 30 or 100.

I would happily work on something like this for free

Well, the context of working within a company is different. Especially if you rely on the money you're making.

It depends on the company but I would say the thing about Washington and this article makes this point well is that there are a significant number of people actively trying to prevent you from doing anything big because they disagree with your goal. In a company, that's less often the case, although I have seen it at larger places.