Good info Bruce. My first job was with an infamous three letter agency (ELT), They don't provide WPs for employees, because they can't as they have no assets to speak of and only a handful of Thai staff that they actually employ.
They do offer every teacher a WP at interview, but they will only provide them for a select few who work in one of the government schools that they farm teachers out to. Yet, contrary to the way Bruce tells us it should work, the school pays the agency, who pay the teachers (anything up to 3 weeks in arrears). Make no mistake, with ELT you are employed by the agency as they hold the (WORTHLESS in effect) contract and they routinely subject teachers to working weekends and evening to make up 100 contact hours. They even have the nerve to limit the number of contact hours each teacher does in the regular school week to ensure they have plenty of staff with hours to make up that they can send to their backwater cowboy English language schools (EnglishPlus) and even cajole teachers into teaching their ridiculous cowboy TEFL school.
Now, this thread is about agencies in general - but ELT are a lesson in what you should not accept. As Bruce points out, should anything go wrong (illegal firing to save holiday pay, transferring from school to school miles apart at next to no notice, reneging on overtime or bonus payments - and ELT routinely do all of these!) then you will not have a leg to stand on. If you are one of the lucky few that have a WP, good luck with single-handedly trying to get a government school to accept liability (not impossible, but most of them have connections they can pull to some extent - often more so than private schools and they are government institutions ultimately!) and if you don't have a WP then ELT have even threatened teachers with "shopping" them to the Immigration department!
There are great agencies in Bangkok, I have worked with teachers who are "properly" farmed out to schools by agencies - whereby the school pays a fee to the agency and the school basically employs the teacher. To some extent this is even a better situation than working directly for a school as the benefits should be equivalent and if things don't work out then the agency can always help you to relocate to another school.
From my experience, teachers working for agencies should expect nothing less than equivalence with teachers employed by schools - WPs, holiday pay, 12-month contracts, sick pay etc. Unfortunately the reality of most agencies I have encountered is nowhere near this level!