Off the top of my head, dogs eating something like pizza crust creates a lot of crumbs (more than a quick training treat for a reward would) which is inconsiderate to restaurant owners and staff.
Some dogs make a good deal of noise when eating/chewing on stuff which can be off putting to other patrons. Diners can be grossed out by a dog possibly licking your hands while they're taking food from you and then seeing you eat with said hands, again a training treat is a lot neater and more subtle.
It's also not good to have your dog looking up for food as if they're begging during public meals.
The dog is there to be working, and other people don't want to feel like you're there sharing your dinner with your pet, they want to see a working dog focused on their job, which is what they should be seeing.
I don't think it's a huge deal to give your dog a treat or reward during dinner, but if you're putting a plate down or giving them a big steak bone or constantly handing them tidbits while they eagerly stare at you (or letting them lick barbecue sauce off your hands) it's pretty obnoxious.