These rules are fine. Banning Clerics, Archivists, Wizards and Artificers would probably be cleaner, but this works too. Although I agree that the Sorcerer needs class features: Draconic Heritage and bonus Draconic feats seems logical enough. I'd probably just use the Pathfinder Sorcerer - it has flavourful abilities (and gets to choose its bloodline!) and doesn't totally suck all the way to 20.
Also, it's kinda dumb that players assume they should get access to every class in PHB. I mean, WoTC has screwed up a ton of things - why should every game be plagued by WoTC's failures, like most PHB classes?