In an earlier life and just once, I took a job via an agency, but on the strict understanding that I would only be employed via the agency then the company would either employ me direct, or I would be gone. The three months almost arrived and I reminded the manager I would be gone the following week, unless they offered me the job direct. They moved very quickly.
My partner took a job at a local school via an agency. The school were complaining about what the agency was costing them, so she suggested she work directly for them instead. She now works directly, on a permanent contract and on much better terms - she gets paid a salary year round, but does no work during the school holidays. Working for the agency, she would be working on other jobs during the school holidays, or not get paid. The only thing - she has to take her holidays during the school holiday times.
We have a cleaning company, (not an agency but a bona-fide company), in work who work similar contracts. No work for the majority during school holidays but the manager and supervisor work those dates at standard worker rates, thereby working for less but also still expected to do their managerial/supervisory paperwork. I've told them to contact their union or ask the education authority to employ them full time.