>How did the middlemen get so much power in the US economy?
I think it's always been this way. It takes a lot of work and resources to deal with individual customers at scale.
>Staffing firms, real estate agents, car dealerships, attorneys, healthcare, etc.
Staffing firms, real estate agents, and attorneys are not unique to the US at all. Staffing firms are used by many companies because they don't want to hire full-time HR people to do "talent acquisition". (Personally, I haven't had good experiences when I've tried interviewing at these companies, and have always done better by going with companies that do their own recruiting and hiring.) People selling their house don't have the time or resources to sell it themselves usually, dealing with all the prospective buyers. And attorneys are pretty necessary if you have non-trivial legal issues anywhere.
Health insurance isn't even unique to the US; lots of developed nations have systems that look sorta like ObamaCare. But they all do it MUCH better, with FAR lower costs. Someone's probably written a long book somewhere explaining why the US is so uniquely bad here.
Car dealerships aren't unique to the US (how else are you going to buy a car?), but the requirement that they be independently owned is, and adds to the cost of cars in the US, and I think especially results in a lot of (less-than-savvy) customers being ripped off with unnecessary charges.
The thing I see about the US is that it seems to be uniquely bad at actually fixing problems. Most of these middlemen services you list are natural outcomes of real-world constraints. A company that makes milk, for instance, can't realistically sell it individually to customers all over your city or state, so they sell it to distributors, who distribute it to their retail stores, where customers buy it to take home. Similarly, a small car manufacturer, like Studebaker, can't set up dealerships all across the US, so they partner with local dealerships that are probably selling other mfgrs' cars too. Back in the early days of cars, all the carmakers were small, remember. A century later, they're mostly big, but the US made laws long ago requiring independent dealers, and now they can't change.
For whatever reason, as time goes on and things change, the US is uniquely bad it seems at adapting and fixing the problem. In better-run countries, they'd see this independent-dealership law is no longer necessary, and change it. In the US, it stays, because car dealers are politically connected to local politicians.