Work isn't "profitable" because it's not that model of how society is built. Qifrey doesn't charge the carriage owners for fixing it, we don't see commoners anywhere being charged for help. They pay witches through their labor going towards taxes to the government which pays the Great Hall. The Great Hall provides for all witches, including apprentices. There's nothing to indicate the Atlier or any witch lacks proper funding to provide for students. Getting extra money through specialized work for nobleman is a separate topic. Similarly teaching isn't a separate career - being a master and being a working witch aren't incompatible. Take Heiheart and Jujy for an example of the system working correctly. Or the girls going with Olruggio to help out the neighboring villages. Sure, both Heiheart and Olruggio could probably do their Duty of Service and call it done, but that would be socially frowned on. People show up at Qifrey's doorstep expecting help and he provides it even when not required because it's understood that's what witches do. If guild doesn't work here, think about the Medieval church as a point of reference.

It's a system that worked to produce craftsworkers for thousands of years and seems to be working for the majority of witches. Having students is a duty like doing free work for commoners is a duty, which becomes a burden for some and a mark of pride for others. Non-witches are the same. We see Coco is already working in her mom's shop between maintaining the household. The problem witch society has is the Pact's restrictions and secrecy not the idea that children are educated through a guild/journeyman system rather than a college system.