That is a fantastic idea. Thank you for sharing. I just checked a few trails that were missing in OSM and they all showed up as bright yellow on heatmap.
Strava even has their own fork of the OSM online editor iD[0], that uses the heatmap data to align (or "slide" [1]) paths to where people have been. I haven't used it in a while, it was pretty slow when I did and I don't know about licensing etc, but it looks like it still works. So if you want to add the trails you could try it out.
Slide unfortunately hasn't worked for years. Not long after Paul Mach, who created slide, left strava, there was that whole national security incident with the heat map.
The heat map was changed to hide military bases, etc, but it broke slide and no one cared enough to fix it.
This is incredibly unfortunate because Slide is ideal for mapping trails in the woods. Lacking something like it I end up tracing them by hand, which is a pain. (I do a lot of trail mapping in Michigan.)
https://www.strava.com/heatmap