Hi, I can see the good motivation behind this, but those maps made a choice not to show the hiking trails and using name= tag for this purpose is kind of like hacking the information in. This will then also cause problems for other maps that do not expect this. Generally there is a rule 'one feature, one OSM element' and so it's better to keep those as hiking relations.

You can add this layer to Gaia that will show the hiking trail overlay: https://www.gaiagps.com/maps/source/openhikingmapHD/

Or use other apps that were designed to show the trail information like Mapy.cz https://en.mapy.cz/turisticka?x=-72.5859911&y=41.5193115&z=15), OsmAnd (https://osmand.net/blog/routes/) or Waymarkedtrails https://hiking.waymarkedtrails.org/#?map=16.0/41.4531/-72.9287)
