Me! Three months ago! And I’m a guy in Seattle who is very inexperienced with non-English travel destinations, so that goes some way to answering your “is it practical” question 
First, some practical details.
Your location says San Francisco. There is a direct flight from SF to Wuhan, and from Wuhan it is a 1h20m flight to Zhangjiajie, which is close enough to serve as a base for your hotel, etc. That is how I got back to the States, although my overall travel was a complex work trip and involved spending a week in Wuhan and a week in Australia prior to China. So it actually isn’t that inconvenient a location to get to.
But … I had timed my visit to the Wuhan office well and was invited on this team excursion, so I was just one Western guy traveling with about 20 Wuhan local software developers, most of which speak good English, on this organized three day tour. That made things incredibly easy. I didn’t have to plan anything, and just went with the group. It also meant that I didn’t understand anything the tour operator said, she either couldn’t or chose not to speak English. No complaints, I was a late addition to a tour that was already planned for Chinese speakers only. It didn’t really matter, the parks and attractions speak for themselves, and I could supplement it with my own research.
I have to assume that there exist tour packages geared towards English speaking foreigners (TripAdvisor seems to mention some), but I don’t have any experience with this. Personally I think I would have found it very difficult to handle local transport, hotels, food, park entrance, etc. by myself. The parks with these landscapes are in rural China but they’re very popular and the surrounding towns have a lot of tourism infrastructure. There were many, many people around. But the tourism infrastructure was definitely catering primarily for domestic tourism. I saw very few other Westerners at these parks, and the ones I did see gave me a strong “I’ve been backpacking around China for years” vibe. Unlike say Beijing or even Wuhan you’re probably not going to find say a Hyatt Regency that’s designed to be easy for foreigners. This was a little bit of an amusing contrast, since both the most basic hotels (but still clean … ish) and the most opulent hotel (in Wuhan) I’ve ever stayed in were on this trip.
Otherwise, once you’re in the actual parks you’ll have the same sort of infrastructure you’d expect in a big US national park: shuttle buses that take you to the various sites, concessions, etc., and its pretty obvious how to navigate it even if you can’t read anything.
Second, my impressions of the place.
It really is as amazing, majestic, and beautiful as you’re imagining. The formations are stunning, and pictures don’t do justice to the sheer scale of it all. The “Ten-Mile Natural Gallery” at the foot of the Tianzi Mountain is a spectacular introduction to them. It’s essentially a valley surrounded by the formations. At the end of it you can hike up the mountain itself, which is a good way to get away from the crowds.
Tianzi Mountain itself is pretty spectacular. Apart from the views of the formations already mentioned, there are some really interesting arch formations and walkways skirting the sides of cliffs with incredible views.
One impression I had was that the philosophy of pristine preservation I associate with US national parks is relaxed significantly, and they’re happy to build huge tourism infrastructure projects. I mean, the landscape is 99% preserved and natural, but they built kind of crazy things too. There is a set of 20+ long escalators in a carved tunnel that takes you to the top of the mountain. They’ve built walkways hanging off the cliffs in many locations, with glass floors in some locations. We took a 7km cable car to the top the one day, and a shuttle bus down the craziest road I’ve ever seen. That was a day full of both exhilaratingly beautiful scenery and a terrifying awareness of gravity.
So they’re building for the expected crowds. You can get away from them if you’re prepared to hike a bit. We did that, and it was really nice.
In summary, I’d recommend it. This isn’t something I would have thought to plan myself, so I was very fortunate to get the chance to do it in such a planning free way.