The distance thing estimate from steps is worthless anywhere but the step count is only worthless if you don't care or can't live with it being a bit inaccurate. As a motivator it's great but the distance of the GPS is probably a better motivator in the mountains. As for my daily walks, while some people log them with GPS I find this overkill and step counting works better as a passive, always listening device.
Agreed (on most points)!
I'm extremely motivated by the step counter on my watch. My daily steps target is 10,000 - and (as I write) I've passed that for 183 consecutive days. Since I really don't want to break that run, I will do the required 6 miles or so every day come what may for as long as I can!
However, I always log my walks using GPS. I often quote my distances and to do so using a calculation based on steps would seem very unsatisfactory.
I'm not sure about the relevance of mountains. My wife and I did a non-stop 50km walk a week ago which was far more demanding than any mountain walk we've ever done. And motivation was very much based on the distance being displayed on our GPS watches!