I won't weigh in on whether tall tees are "cool" or not, but I am perplexed why so many people change their personal style up so significantly between on and off the hill.
It seems to me that if you prefer big, baggy, and tall clothing on a daily basis, it makes sense to get outerwear that reflects that. If you like fitted clothing, or even just average fitting clothing, why not wear that on the hill?
Better still, how about wear what's functional, comfortable, and what you personally like. You don't need the greenlight from NS, man. Don't worry about it. Chances are that if you need others approval to do something, you're not all together comfortable with it,