Because there's nothing remotely like that in Burke's Garden.
What you have with the place is a 20,000 acre valley that sits at 3,000 feet above sea level. This valley is drained by a single tributary, which prevents the place from being Burke's Sea. The entire valley, save for that one water gap, is surrounded by mountains that tower anywhere from 4,000 feet to almost 5,000 feet above sea level. Burke's Garden itself is very sparsely populated, with only around 250 humans living there. It's an agricultural community with lots of farms and many head of livestock. Parts of the place must be quite ripe in warmer weather. I wouldn't drink the water in Gose Creek (which drains the cattle-heavy expanse).
I took this video standing beside what seemed to have been, at one time, the single elementary school in the valley. It was a school day and empty, so I assume it's closed down, these days. In addition, the community has located a series of garbage dumpsters on the site, so I guess they don't expect the children to return any time soon.
There is only one shop of any type to be found there. It's a quaint general store with some food and beer and a small grill, etc. The lady running it was very sweet. They have a single gas pump. Unleaded regular, I reckon, but I didn't need gas, so I didn't look to see what they had. We bought some firewood there and some chocolate-covered peanuts that totally rocked. I do recommend a stop there--the people who run it were most kind.
There is one paved road leading into the valley. I would suggest that you take that one if you are driving a conventional two-wheel drive auto. We came in from the east on a Forest Service road, and even with my four-wheel drive and high suspension Frontier it was pretty rugged. I guess the budget for Forest Service road repair is rather tight in recent months.
Another reason I wanted to see this remote community was for a single road sign. I'd heard about it and seen one photo of it and I wanted my photo taken standing under it:
I'll be heading back to Burke's Garden in the future. The Applachian Trail skirts the south side of the valley and there's a really isolated wilderness area there called Beartown Wilderness. I'll definitely return. Sooner, hopefully, rather than later.