That seems like a bit of a “Trolltag”, no?
(/nbr “not being rude” /genq “genuine question”)
Luckily many of the occurrences have other tags that make them ignored for routing (like access=no or disused:highway=* with no highway=*) so the tag is merely redundant rather than actively bad
Sorry - I should have been a bit clearer. Why would it make sense for someone to use that tag instead of (or in addition to) a bunch of other keys that might suggest that a way should be less likely to be suggested?
This is just a case of routing algorithms being less intelligent than a primary school child who knows how to safely cross the road using the Green Cross Code. We should not be tagging to please bad algorithms 
The footway=link tag was new to me. Having now read the documentation, I still do not see how this matches the situation that you encountered.
Well, yeah, an implementation of Dijkstra’s algorithm will generally have less cognitive power than a seven year old human being. I’m not sure why this is a surprise.
I didn’t say I was surprised. I said we should not be tagging to please bad algorithms. 
I do not agree that routing algorithms are less intelligent than school children. Of course a school-child can see this when getting there, but not when planning a route.
Routers mostly work on the assumption that everything is mapped. If there is no road close to your starting position, they have to assume that some ways are not mapped (or your GPS is not precise or you parachuted to get where you are).
But apart from that, routers assume that if ways are close but not connected, there must be a good reason for that, even if that reason is not mapped.
I have sometimes tried to outsmart OSM, but most times realized that I am not smarter that my OSM router when I end up where I planned to move from a path to the other side of a road and discovered a very unpleasant and long ditch between the path and the road where I had expected a patch of grass. Or trying to cross a way, that has a big barrier in the middle.
A path that is completely disconnected is something that is easy to generate a warning for. But in general when we add a path we should make sure to connect to other ways wherever we can, not just at one point.
For example, sometimes a cycleway is added along a road without connecting to the road for many kilometers. That means that routers cannot know if it is possible to make a U-turn using the path on other side of the road. Or if a cyclist can make a left turn (right turn for UK), at a 3-way junction on the road.