I was a Contingent (third-party) Technical Recruiter for 2.5 years (and hopefully never again, sans a cool company such as the above) and would love to work in that model. I only had the opportunity with something similar when our sales (the folks who got the requisitions / open orders) had many openings in similar "verticals." E.G. five different companies all looking for Java SE developers, with slight variations, but, for strong candidates I/we could get them several interviews, sometimes multiple offers.

Would be much more fulfilling. In most markets, however, this is (if the relationships are not established with multiple companies (which it sounds like the case in your situation)) "skill marketing" or trying to gain a sales foothold into a company by "marketing" a candidate to the company. At one of my former employers, the relationships were solid enough to where we created a few positions for some great candidates as we understood the departments needs. This is not typical at all, so finding a few companies actually making this a standard model would be fascinating (I imagine boutique retainer-model recruiting).