Why would Highway=path/footway be different from other highways in this regard?
On all other highways, they get a name tag if the road has a name, even if we divide the road into separate ways for bridges/tunnels/differing surfaces/etc. and then if there is a ‘route’ that happens to share the road (ie state way 101 is concurrent with Main st for a while) it gets added as a relation.
Saying every trail needs a nameless way and a route relation seems like a lot of unneeded complexity in 90% of cases.