Early in my career I worked for a consulting firm as an employee, and I never found out exactly what I was billed at but I'm guessing it was around double what I was paid. We worked on site at our client's office, and people there called us "contractors," but we were employees of the consuting firm. We had benefits, training, overtime pay, etc. and we got paid our salary between jobs when we were not on a client project.

If I were an indepenedent contractor using an agency to find work, I'd expect them to take a much lower cut, as they have much lower overhead and risk.

You can find recruiters that will clip a small fee and dump you through a contractor management platform. It's all automated. You're effectively a freelancer, still need to sell yourself a bit to get hired but the recruiter vets leads on both ends to streamline things.

Contracts are short and sweet so it's not like interviews are multiround or anything, 15 minute coffee with the client to check if you're aligned on stack / interest and off you go.