Yes, the tags of the features inside of a park/preserve are important. But think about it from the perspective of someone from out of town who is searching the map for a place to go. If they want to look for a good place to hike and see nature, they wouldn't want a more managed park to come up in their search. Similarly, if they were looking for a park for more general recreation, they probably wouldn't want a nature preserve that is meant for hiking to come up.

I very much appreciate the work that you have been doing for the trails in the region. But working on tagging is something that can and should happen concurrently with collection of new data, especially when there is a dispute.