While I personally wouldn't use a twisted wire bit such as these we are talking about, because I ride trails and wouldn't want to take a chance of injuring my horse's tongue if something unpredictable happened, I won't condemn those who do if they are responsible about it (for instance, a respectable trainer).
What a stronger bit gives you is respect and finesse. It allows you to have a horse you can guide with just light rein contact or even just the drape of the reins.
If you don't have secure hands yet (and we all were that way in the beginning), then use something mild to protect your horse's mouth while you learn to ride. (What I did was simply stay out of my horse's mouths and rode on a loose rein in the beginning.) It took me years and years to feel comfortable riding two handed with contact. To know I was ready for that step and had soft hands.
And if you get great results in a plain snaffle, then by all means, stick to that.
But I get irritated by the "snaffle or nothing" mentality because stronger bits do have their place. They are for finesse. Try as I have, I just don't get the respect out of a plain snaffle with my Mustang. Sure, I can ride him in it, but I have to pull on him harder than I want when he dives for grass or we canter, etc. I put him in a curb, and he is super light and responsive and like putty in my hand. I neck rein and ride with a loose rein.
I could see, how if I always rode in a plain snaffle, my horse would start loosing respect for the bit, and getting a tough mouth because he would learn to ignore my subtler rein signals. Not that I was rough with my hands or he didn't know the signals were there, but because he would learn he could ignore me if he wanted to. He could call my bluff, as it were.
I don't want to have to pull on my horse's mouth. I want him to respect me and comply. Power steering, power brakes. I like the light, collected feeling of a trot and canter with a curb, and at the walk I can totally give him his head.
Yes, the double twisted wire bit looks wicked and I personally wouldn't use it, but I could see a trainer or someone using it in a responsible manner to keep the horse light and responsive.