I think this is right for tagging, likely all desire paths are also informal (but only because I can’t see any need to tag the origins of some paths & roads as desire lines: see my earlier post).
It’s also really useful in England and Wales for creating new public rights of way. If one can show the public has used a path for 20 years or more, without obstruction, then the route can become a public right of way (legal access for the public even on private land). Having a path mapped is one way of showing its existence and use.
I didn’t use to bother mapping desire paths but, for the above reason, I now do.
Edit: but to stay on topic. Yes, I think current tagging is sufficient and it is down to routers/map providers to distinguish desire paths against formal paths (if they or their users wish).