I was thinking this too recently. But the entertainment is a little bit different. Jobs are shorter (even TV shows take only a few months) and talent agents get 10 % of all your work - but would you pay your IT agent for 2-3 years (I'm guessing the average length of a programmer's tenure at a single company) 10 % even when he literally does nothing most of the time?
Ideally, my "agent" would have max 2-3 other candidates, and offer a totally white glove service: They know my comp preferences, my location (or remote) preference, my ideal company size, industry, desired job level. They would know my schedule and go out and do all the searching and filtering, the application legwork, and basically only get back to me when the interview is scheduled and I need to show up. Then, afterward, they would take care of all the salary negotiation/maximization and let me know the offer and starting date. I'd probably be willing to pay 5-15% of my first year's salary for that level of service.
Don't quote me on that, but as a rough approximation, I feel like the toil of job hunting is so extreme that I'd be willing to part with a significant chunk of change for someone who could actually reduce that toil and deliver a real job offer or two.
I'm not sure why there aren't any "free agents" running around Silicon Valley like they do in Hollywood. If I had to guess, it's probably because the same skills you need to do that job in Silicon Valley pay more in other sectors, like Hollywood.