Riding with a neck rope is much more controlling (esp if it stiffer/higher). But it cannot allow for lateral flexibility (even with correctly place leg aids) nor longitidnal flexion.
Very good point that various different types of equipment are used/more appropriate for different styles, etc. But I don't understand how you mean a neck rope is 'more controlling'(than what??).
I suspect that you're saying you can't teach lateral/vertical(longitudinal?) flexion with a neckrope because you can't really force it like you can with a rein attached to the horse's muzzle, but that's not to say you can't teach it - you can teach a horse to flex without any strings attached, so you can definitely do it with the help of a rope around the neck.
Are bits harsh? It totally depends upon the hands which hold a bit or a bitless bridle or even a neck rope.
I agree... and disagree
. Any equipment can be used roughly and bits can be used sensitively & without being at all harsh. But they are a piece of tack that are very easily capable of strong pain, be that because someone's rough, unskilled, the horse is not sufficiently educated, accidental.... that's why I like to start horses - & novice riders - in a halter or such, to reduce the likelihood of hurt due to mistakes. Then if desired, the horse & rider move on to a bit when they're soft & reliable without.
Can a fully trained horse be put into a neck rope to show off? Certainly. Can you get to the same end with it? Not imho. Good enough for some circus work? Yes. Ability to do jambette training? No. Canter pirouettes? Not in a refined way
I think this is probably getting beyond the scope of most here - including me - I aspire to that sort of level, but... not quite
But to say things can't be done except for showing off & 'some circus work' is just fooeyness. If you aren't aware of what sort of levels can be achieved without a bitted bridle, you might want to 'youtube' Mario Laraschi, PF Pignon, 'The Flying Frenchman' Lorenzo, Honza Blaha, for eg. While if you're a good trainer/rider, you can do those sorts of things in any headgear, I think getting the same level in a neck rope or without anything proves