In freelance tech recruiting, the jobs are the scarce resources, not the candidates. Freelance recruiters focus their effort on obtaining new positions for them to fill in, and only then they look for suitable candidates. You can see that in how they angle to find out about other companies that you're interviewing in - they do that, because they very much need it as another lead.
In other words, nobody would care about becoming your agent, because you're fungible. That's why it's not done in our industry. I suspect actors are much less fungible (you can't cast a 20 years old white cheery woman to play 50 years old broody black male who can ride on horses and do a british accent), hence market dynamics are different there.