I think you mean the line "corrective techniques and tools?" I meant corrective techniques and corrective tools, just didn't make it super clear. EG a collar pop would be a technique, while a prong would be a tool, but you don't necessarily have to use collar pops if you are using a prong.
A good force-free/reinforcement-based trainer, just like a good balanced trainer, is going to listen to the dog and see what the individual in front of them finds aversive. Many dogs do find head halters inherently aversive - they display avoidance behaviors around getting it put on, try to paw it off, maybe refuse to walk in it, etc. They can also result in neck damage if you have a dog who lunges hard and give them too much lead so they hit the end and snap their head around. Easy walk and other harnesses that tighten when pressure are, yes, also capable of causing damage. Both of these are rather controversial among force-free trainers, and many won't use either. It's not like everyone who prefers reward-based training has exactly the same opinions, approaches, and experiences, after all!
That being said, sometimes you need a tool for short-term management of a problem to keep dog and handler safe, and need to make some concessions. Say I go out and adopt an adolescent large-breed dog in January - right in the middle of icy season here - and he has zero leash manners. I need something right now, in the short term, to manage his leash walking to keep both of us safe. Ideally, we'd still be training alongside the management tool so we don't have to use it any longer than absolutely necessary, reducing the possibility of injury by reducing the time the dog has to spend in the tool.
Personally, I'd look at the dog, his behavior, and what he finds aversive or not. Does he pull pull pull but doesn't do a whole lot of lunging or show reactive behavior on walks? I might try a head collar, introduce it with as much counter-conditioning as I can to reduce the risk of him getting distressed by wearing it, and just keep him on a relatively short lead. Does he hate the head collar but respond well to a front-clip harness? I'll go with the (non-tightening) front-clip harness. If that doesn't work well enough, maybe I'll try something like an Easy Walk, assuming he doesn't show any signs of the Easy Walk being aversive or highly uncomfortable to wear. Still having trouble? I, personally, may try a prong at that point (ignoring the legality for the moment in this hypothetical). I can't train this dog to walk nicely if I get dragged down the icy stairs to my apartment and wind up in traction (and might even need to rehome him in that scenario), so using something that works causes pain might be worth it just to get past the early stages of leash training with both of us in one piece.
I should mention here that I follow more of a LIMA (Least Invasive, Minimally Aversive) philosophy than some reward-based trainers, in that I will consider corrective tools/techniques in some scenarios where less invasive/aversive solutions aren't working - like the one above - where others may not.
The difference between the head collar and non-tightening front-clip harness compared to the prong is mainly that, when used correctly, the first two should not cause pain. They work by making the dog unable to put force into the pull, because forward momentum gets redirected to the side. Throwing their weight forward just swings them around towards the handler. They have risks (especially the head collar, imo), but when introduced appropriately and the dog's typical behavior and responsiveness to the tool is taken into account, you can minimize that a lot. The Easy Walk is kind of in-between. It does cause discomfort as well as redirects the force of the pull, that's the whole reason it tightens. With prongs, causing pain/discomfort (depending on how sensitive the dog is) is why it works. It doesn't do anything to redirect the physical force of the dog's pull, and relies entirely on pulling against the prongs being uncomfortable enough that the dog decides not pulling is better.
Obviously, success with any of these tools can also depend on the training used alongside them, and the prong is the only option listed that allows for collar pop style corrections if that's your thing, but for a fair comparison I'm just talking about the passive effects each tool has on pulling that would give immediate results in this hypothetical scenario where I'm looking for an immediate solution to allow me to get this dog exercise without killing myself on the ice.