Um, no, that quotation means literally the opposite: it is about the climbing, it's not about getting to the top of any particular mountain. What Hillary was getting at is we get satisfaction from learning, training, overcoming difficulties and limitations, and ultimately pushing ourselves to our limits. His limit was Everest, your limit might be Snowdon, but it's climbing it that matters, not just taking the train to the top and taking a selfie.

Should we ban people from taking the train? They get a different experience, but they still get an experience

No, but we should mercilessly laugh at them for calling themselves mountaineers when they are train-riders.

He's saying that you can substitute any activity that combines danger, skill, and willpower for the mountain. It's literally not about the mountain, it's about how far you push yourself to reach a goal.