I don't think your hypothesis is correct. There are sites out there that already aggregate the permanent and contract markets. (i.e. itjobswatch.co.uk) - I'm sure others exist for other territories. I know its fashionable to bash recruiters - and man do a bunch of them deserve it. But for contractors/freelancers - if you don't like selling then service companies/recruiters are your friend. Quit thinking of them as us…
That's not precisely how it works, but companies accept there's a recruiter fee in the cost of a permanent hire, but will have a salary range they can offer, usually set as a policy by HR to stop wage inflation. Also the recruiter fee then is seen as a one-off cost.
For contract wages, companies tend to have an all-in price they're willing to pay, which they'd happily pay the contractor directly. At that point, the recruiter is usually taking the difference between that and what they pay the contractor. In most contract positions (in the UK) via recruiters, invoicing is done via the recruiter.