This! While a mountain bike and a road bike are both types or kinds of bicycles, the roads they can travel on have properties that aren’t symmetrical. That is, while one can also ride an MTB on a =cycleway, the converse does not hold. You can’t ride a roadie on a way constructed or intended for MTBs.
Secondly, I think there is some confusion between a path “purposely constructed [for] MTB[s]” mentioned by @Hungerburg above, and a “shared-use path” @ezekielf mentions. If there is a path that is contained in a fenced-off part of a park or forest enforceably meant only to MTBs, it might deserve a “first-order” tag for MTBs (probably in the sport= namespace, and an mtb:scale= of > 1 or 2). All other =paths—whether merely suitable or constructed—for MTBs are also available for hikers.
I do hail from Finland and we have Nordic style Freedom to Roam laws, so that may skew my perspective: here it would be all but impossible to legally forbid people from walking on paths constructed for MTBs, unless they are built on private land and physically fenced off for others.
For both reasons I think a “first-order” highway= tag for MTBs is out of the question.