Fantastic question... I'm looking forward to the answers.
As a breeder, touch sensitivity makes an immense difference for me in determining where a puppy will go and what jobs he'll have in life. I have found it also makes a huge difference since I have 2 vastly different breeds .. so its really not a "one size fits all" sort of answer to the question.
My first breed, Samoyeds, typically have a low touch sensitivity as a whole... but there are, of course some differences between each pup. Generally, I've found that the pups with a higher touch sensitivity are typically a bit quieter and slower to explore... they work better for owners who match that temperament. These owners MUST be instructed to work on grooming on a daily basis or this long coated dog will not be tolerant... this does two things. It stimulates the dog and teaches the dog that it will survive/thrive and becomes a part of the normal ritual of life. The pups with a lower sensitivity tend to be my "brighter" dogs.. the ones out adventuring and learning about new things. They are less reactive to the tugging of hair during grooming and while they need to learn it is a part of life the owner can do it on a weekly rather than daily basis. Samoyeds work best on a paycheck/reward basis generally as far as training, physical styles of training are generally rewarded with a dog who simply shuts down. The high pain threshold/low touch sensitivity comes into play when you are actually working them at their job. A "good" Sam will work beyond what its physical limitations should be... and an owner/handler needs to recognize that pain will NOT be shown until serious damage is done (the dog who runs its pads off while sledding.. and is eager to go again before they are healed.. or the dog who is still willing to herd or run agility dispite the fact that it has torn its ACL).
My second breed, Bernese, are different. In my experience the pups with higher sensitivity are the ones who are out exploring. The lower sensitivity ones are quieter and more sedentary. The lower sensitivy ones are still "bright" but are less concerned about pleasing and you have to find ways to motivate them... redirect them, they make great dogs for someone who is looking for a dog who is quiet and low activity. The higher sensitivity ones seem to be "on" and always looking for direction and attention. For these pups praise seems to be the key to life... they'll work for food but food is not the motivator.. the praise is. Grooming is an issue for both types of pups... the reactive dogs get very stimulated by grooming and find it hard to stand still... the less reactive dogs don't get why they should STAND when lying down seems like a better option.
For the most part my style of training is mostly reward/praise based. For both of these breeds that seems to be what works best for me to get where I need us to go. That being said... when physical reinforcement of basic principles such as "you WILL not bare your teeth at humans" needs to happen, I tend to be MUCH MUCH harsher with the dogs with a lower pain threshold so they get the message in a big dose very fast and we never have to think about the issue again.
Of course every dog is different and there are multiple types of approaches to training.. or in my case, solving problem behaviors. I will utilize touch sensitivity when I believe it will have the effect I desire... i.e: bumping a dog who has crossed into my space while walking on a loose lead and not in a formal heel position.