Yes, it was Kevin Kenny (ke9tv), another Mapper of the Month, who helped to both coin the "front of park / back of park" concept (using leisure=park ONLY on the "manicured" segments of larger boundary=protected_area polygons) but also the word "manicured" and the phrase "human sculpted landscape."

A natural preserve (leisure=nature_preserve or boundary=protected_area) simply is not a "park" (even as that word is blurred in US English with the OSM tagging of leisure=park).  ALTHOUGH, it may contain small (front-of-park) subset areas within it which could be rightly tagged with leisure=park.

The US has been chewing on these topics for many, many years, and Brian, Kevin, I and many others have contributed to the understanding that the "front-of park / back-of-park" concept is quite workable.  It may not be perfect, but I'll take "workable" any day of the week.  It has truly improved things to the point where these "tempests in a teapot" are only on a low simmer, rather than boiling over.

Good luck on the specifics of where the leisure=park SUBset(s) are in this (correctly tagged) leisure=nature_reserve.  Sometimes they include sinuous access road squiggly polygons, sometimes not and sometimes include "islands" that are not obvious how you get to them, but these are geographic data describing "where" (not always "how").  And as leisure=nature_reserve does render the boundary edge, "you get that, too."

If you really wanted a more complete more "pretty looking" map (in Carto, say), you could carefully add natural tags (like wood or grassland) where appropriate.  All together, to seasoned visual parsers of these rendered taggings, you'll "see what's really there," not as the fill colors you seem to want to see with an (incorrect) leisure=park tag on the whole polygon.