Oh, by all means. Normally, I’m the one saying that (since I really want to add more climbing routes) but now I’m in a position to represent the arguments from the “other side”. Oh, well…
Climbing paths actually do have a tag (which, admittedly, I find a bit confusing and too separated from the rest of x-ways). There’s a whole section on climbing, covering all three of the climbing examples.
The glacier routes are also paths. Sometimes quite visible. When not, they are no different to a rocky T6 hiking route, for which we have a photo in the examples.
This is also one way to see it, which I believe @aighes is demonstrating here.
If we agree that a path is a trodden ground in the woods then, of course, we need another way of representing all the examples from