I've been to plenty of national parks with my dog. The rules are generally that dogs must be on-leash, and they are not allowed in especially sensitive areas. Those rules make a lot of sense to me.
The NPS hardly has a vendetta against dogs. At Carlsbad Cavern they even had a free kennel facility so you can visit the caves without worrying about leaving your dog in a hot car.
Not sure where you are, but the southwest tends to have pretty dog friendly policies. Sand Dunes, White Sands, Grand Canyon, Petrified Forest (these are just ones I’ve been to off the top of my head) all allow pets on trails with some minor limitations: e.g. Pets only allowed on rim in Grand Canyon.
Pretty easy to google a list of dog friendly parks.
Alright I guess we just have different ideas of “minor limitations”. Being able to use only a single (paved) trail in the entire park sounds like a pretty major limitation to me.
Regardless, I much prefer BLM and Forest Service land. Free as in freedom, free as in beer. National Parks are fantastic for the disabled and (petless) families, but that’s about it as far as I can tell.
The NPS hardly has a vendetta against dogs. At Carlsbad Cavern they even had a free kennel facility so you can visit the caves without worrying about leaving your dog in a hot car.