I ride my horse with a string around his neck frequently. I first did it with my first horse when I was an ignorant(& invincible, egotistical
) teenager, to begin with because I always had baler's twine on me & often forgot the halter! In hindsight, in his case, I'm sure it was not always beautiful or gentle - baler's twine is thin & strong - and I did take him out like that on occasion. I didn't appreciate just how good a horse I had under me back then.... or how lucky I was that I didn't have any mishaps.
So these days, it is part of their training, that I teach them to yield to pressure in all sorts of ways, in which a neck string is just one more. The last horse I started under saddle I didn't actually use a halter on until he understood the basics with a neck rope. The last few horses I've taken on to 're-educate' I've found have done really well starting off with it before going back to conventional methods they've already learned to have a bad attitude about. Somebody said something about an 'oh crap! strap'
& this is sort of how I use it or reins, in that it's a backup if the horse doesn't listen to legs or seat, not used with any real pressure otherwise.
I think riding like this really helps you & the horse get 'fine tuned', but these days there is no way I'd ride a horse outside the paddock(or arena, yard to begin with...) without a halter - it's all very well to be idealistic & my horses do respond as well to this as conventional reins, but safety comes first & I don't consider riding in the open or public safe without halter & lead.