I am not sure if Tenkara would be my one rod choice, but on a personal level I started using one primarily in the park this winter. The first one I rigged was literally a black widow crappie rod rigged with a monfiliment line attachment (called a lillian) on the end with a mono line and regular leader. I called this Hillbilly Tenkara, to see if I wanted to invest in a regular setup. After trying the mono set up I changed to a furled leader I had a guy on ebay ($15) that sells the line make for me in a 10ft length on my 10 ft rod with 3-4 ft of tippet. It was a big improvement in casting once I adjusted to the new casting style, I think due to more weight than mono. I than ordered a Tenkara 12ft rod, I had the same guy make me a 12ft furled leader and I use about 3ft of tippet on average sometimes more. Furled leaders come with a tippet ring which I use on my regular rods all the time (for me instead of chopping the high dollar leaders we use, with the tippet ring, the ring stays on the leader and you just replace the tippet, no surgeons knot in the middle of the water, just tie a improved clinch on the fly and at the tippet end, attach to ring and your off, cheaper than leader replacement and easier for me in the water to tie.
I have used on a regular basis in the Metcalf area and Middle and have adopted to the style, it is diffrent and has a learning curve. Tenkara was designed centuries ago for mountain streams which fits the Smokies perfectly, as you mentioned along with high sticking the drifts, for me it also allows me to get over a distant fast current and drop it right behind a rock or tail area or any area and just simply lift when it starts to drift too fast. I find I cast less and leave more leader off the water and just the tippet where it needs to be, it also helps eliminate a lot of whipping the water to death and scaring the fish more than I usually do. Because the tip is so small the spring action of the rod does the work when landing the fish and even a very small bow in the Smokies makes for fun, there is no reel so a mix of using the net and handlining will bring it to you. Traditionally they use just a variation of six flys (yes I have learned presentation is everything and has greatly improved my skills with my regular fly rods) but I use the same drys and wets I have always used. Is it for everyone probably not, but for just plain fun and stripping fishing down to basics and broadening your skills and variety it works for me.