> You will understand the need for any route list to have every part with a name.

Unfortunately, that is not how reality works in Austria. There are many unnamed foot paths here, even (or even especially) if they are part of an official hiking route. The way description if you want someone to follow the path is then usually "walk along hiking route Foo" (where "Foo" is the name or number of the hiking route). Or you have to describe the path in some way (that usually requires local knowledge), but that cannot be done by routing software (only by a human walking guide author) and also does not belong in the OpenStreetMap name= tag. You cannot describe a hiking route in Austria with path names alone.