Parents aren’t as au fait with technology and thus feel the need to tell you that not being contactable at all times is “a good thing”. They are wrong. Especially if they’ve taken the aforementioned route to Switzerland.
Taking a mobile phone (and ensuring that they’ve got theirs) avoids wasting time scaling the mountain or warning the French pisteur- secouristes to look out for your lost mum. They’ll probably just laugh at you and compare your mother to a stray goat anyway.