There is no reason to start on a bike bigger than a 250 either. The Ninja 250r has plenty of power and speed for operating on any road in the US. The combination of very forgiving engine and drive train and light weight make it a great starter bike. And due to its resale value you lose little if you decide to sell. Even buying new and selling a year later your cost is still modest.
Bikes like the FZ6R are not heavy but still the 250r is at least 50lb lighter and slightly lower also. This makes it more forgiving when you make a mistake at slow speed maneuvering.
I’m 6’2″ 220lb and the only real disadvantage to the 250r is it is a little cramped for my legs.
Still the FZ6R is a much better bike for a beginner than the supersports despite sharing an engine configuration and size. It really a combination of engine tuning and riding position that make the supersports so ill fitted for the task.
The GSX-650F is considerably heavier than the FZ6R which makes it great for a small sport tourer but I could see that making it more of a handful for the beginner. I know I’ve caught my bike several times when I’ve made a slow speed mistake.
The Ninja 250 is light enough I can easily recover from those types of mistakes. And because it is easy I can also push myself more in those situations speeding the learning process. That I see is the big advantage of a small bike to start. It allows you to learn faster with confidence because you are not as scared of the bike.