The answer is no, talent agents are not exclusive to actors. Many other "highly paid" professions have agents: sports players, musicians, actors, authors, for example. But most of those professions make significantly more than software developers, so anyone just out to make a buck (and most middle-men are), is going to go after those bigger fish.
I have read over the years about several companies that purport to attack this problem more like talent agencies. Probably the one that made the biggest news splash is 10x.
Software development is clearly lucrative enough that plenty of "middle-men" are making money. Especially if they can automate the process. That's what sites like upwork and xplace are doing. But there's a full spectrum. On one hand you have complete automation, and on the other you have a dedicated sales team.
Any software company of more than even a couple of people usually has someone whose full-time job is to manage client relationships and close sales. It's not uncommon for agencies to have even 50% of their staff devoted to sales. So I guess my point is that sales is hard work. It's easily a full-time job. If you have so much extra work that you can skim 15-20% off the top, maybe consider hiring a subcontractor to bring in more sales?
It's worth noting that recruiters hear about more jobs than you do, and some percentage of those jobs are open to contractors. They are few and far between, however. I respond to any recruiter that contacts me on LinkedIn that sounds like they probably actually read my profile, politely telling them about what I do, and promising a conversation if they have a real opportunity that matches my interests. (Only a few have ever replied, but I have gotten one decent gig that way.)
Ultimately, there's really nothing like leveraging your own network. Anecdotally, I went almost three months looking for work at the beginning of 2016, and when I finally posted on twitter that I was looking for work, it came pouring in. This may have been a coincidence, but who knows!