So looks like I've never read the wiki page for parks…

I've worked on some of this sort of tagging with https://www.openstreetmap.org/user/ElliottPlack in Baltimore. The tags we landed on were boundary=protected_area, protect_class=5. I think protection_title=City Owned Park would apply as well. Wissahickon Valley Park is tagged this way (by me), but I guess that shouldn't be a leisure=park. Unless something's a designated nature reserve (e.g. https://www.openstreetmap.org/way/484364316), I wouldn't tag it as that. boundary=forest also doesn't seem right.

My opinion on Rolling Hill, Kenealy, and Mill Creek is that they aren't for the most part leisure=park (exceptions are the Richie Ashburn Field part of Kenealy and the dog park and parking area of Rolling Hill).