But if you are here on an H1B you don't actually have a congressman. The US citizens you are competing against do. And this is why the system works the way it does.

You have a congressman. That is, you have representation but not suffrage rights. Congresspeople will assist with making congressional inquiries. Their political incentives are a separate matter, but even advocacy ultimately has to get to the legislature. The failures of the system aren't a result of the H1Bs v/s US Citizens dynamic. In reality, there are several different groups with their own incentives. Kind of like how failures of US healthcare isn't a patients v/s doctors dynamic.

If I have a green card I can donate to political candidates though. I don't know how many dollars is equivalent to one vote, that probably varies by candidate.

So H1Bs are also competing against green card holders with more political power than them, not just citizens.