Yeah, I realize I've only been in the arts for fifteen years, but I've never met a school, even the ones I find to be more about exercise, or the ones that are more art and less martial, who does "no contact" sparring. I've seen light contact, where the aim is to thump rather than injure, but I didn't realize no contact was a thing...
As far as resistance goes, I think of it on a scale, with about seven steps:
1. Facilitation - The opponent reacts intentionally in the desired way. Only for isolated demonstration purposes, NEVER for actual training. Unfortunately, difficult to avoid.
2. Accommodation - The opponent allows themself to be manipulated however is desired, but does not in any way assist or resist. Useful when first practicing a technique, but not for long-term training.
3. Resistance - The opponent attempts to remain as they were, but initiates no actions of their own volition. First test of technique learned with accommodation. Useful for long term training, allows detailed technical study of what is possible, but not what is feasible.
4. Neutralization - The opponent attempts to escape, avoid, deflect, or stop the desired effect. Good test of practicality of technique. Essential for long-term training.
5. Counteraction - The opponent not only attempts to neutralize but also initiates technique of their own. Develops adaptability and increased awareness of feasibility and practicality. The essential standard for long-term training. This is basically sparring, but not a full-fledged, competition levels of contact.
6. Aggression - The opponent counteracts but with full intent to injure or subdue, either in unavoidable real world combat or a close simulation.. The best reality check, but inherently dangerous. Essential for serious long-term training, but to be used extremely sparingly and only among experienced practitioners. This is full-contact, full-force sparring, essentially.
7. Assault - (This one is illegal, and for good reason.) The opponent utilizes full aggression, but is beyond normal human mental states, whether due to drug use or extreme emotional or neurological states. Only in unavoidable real world combat. Never for training, due to extreme danger, impracticality, and issues of morality.
No contact isn't even on this spectrum. It's its own beast, and I'm not certain why anyone would do it.
I really don't understand the "is kata useful" question that comes up so much. Kata is nothing but a way to remember a whole ton of two-person drills, as well as a platform to spur innovation into new drills, all of which should then be incorporated into your sparring. I assume we're all a fan of two person drills, and I further assume we all are fans of practicing those two person drills alone, when we really want to perfect them, or have no partner at the moment. I don't understand how a Mnemonic pattern for remembering those drills becomes such a source of contention for some people...
People focus on the actual, lengthy, one-person dance part of the kata, and forget that actually doing that dance should be a fundamental, but otherwise small part of your training. Analysis and application should, in my understanding, be where the vast majority of your kata training time is spent.
If you're art is kata-based, then take what you learn from kata, and experiment with it, test it, experiment, test, refine, abandon, or assimilate as needed, at varying points of resistance along the spectrum from full cooperation to full opposition, every level short of all-out assault has it's place in true training.