The above question is very common and likely most dog training instructors have had this asked of them by students. The idea of using food to train has not caught on for many dog people likely because it is misunderstood. EVERY student I have had has asked this question at some point during the training process.
When I get asked this question I try to put it in perspective. Often, the question will be followed by ” because I won’t always have treats or a clicker with me”. One way I explain it is by reminding the student that the dog is already on a leash and collar which technically is a training tool. One could ask “When can I get rid of the leash and collar? It is no different. What is different is the way treats are viewed.
The point is this: Leashes, collars, food, harnesses etc are all training tools. Often one gets hung up on the idea of food as a treat, when in fact it is a training tool.
When training a dog, one can “get rid” of the food rewards when the dog is doing the behaviour to your satisfaction. HOWEVER, even highly trained working dogs have on-going training during their entire working lifetimes in which they are rewarded (or corrected if using aversive techniques). If you want a behaviour to be sustained, it will benefit you to keep food on have and occasionally give a reward for correct behaviour – just as working dogs are rewarded during their training and aggressive dogs are sometime not let off leash or corrective collar. No different.
My advice to new dog owners is to see the food reward as a training tool that you use to teach a behaviour and then keep it at a level that you want it. You won’t be giving it continuously if you train correctly, but occasionally you can do a training session to keep the dog on his paws so to speak.