"I've always wondered what their ultimate collective bargaining power is if the single thing that grants them their leverage (to strike) is off the table from day 1."

While they can't strike, they can do the absolute bare minimum, which is what happens in a lot of professions (police, fire) where they can't legally strike. I'm not saying it's as effective as an actual strike, obviously, but with how much extra time teacher give beyond normal working hours, cutting it down to just working during business hours makes a school noticeably worse.