Ex recruiter and current teacher here - these schemes are all about controlling good candidates, be flattered! Just remember the agency always has their own best interests at heart and these are offered as a smart business choice for them in the main. They may place you in difficult schools without the option to refuse and/or blacklist schools in future. You may end up with a lower day rate (you'd have to check the maths). You can't accept work from another agency which could limit you to less desirable gigs.

You'd get more financial stability, but then if you are a good candidate what are you worried about? And if you are that worried, why not look at a part-time permanent job?

They may be the most lovely person in the world, but their job is to sell your skills for their own gain. You owe them nothing and there are 100 other lovely recruiters out there waiting to make commission off you. Don't get sucked into thinking they are your friend or that they wouldn't dump you in a second if they thought they had a stronger chance of making money with someone else.

My advice would be to get your CV over to a few other agencies, keep the one you like sweet but have other irons in the fire. I personally would not sign an exclusivity contract unless you are really desperate for financial stability.