I feel how light a line you can fish is at least partly determined by the wind conditions you fish under, the wind resistance of the fly patterns that you are casting, and the size of the fly patterns you are throwing. In each of these instances more line mass helps a lot in getting the fly to where you want it to be. So I do not see going to the lightest line you can possibly cast as being the ultimate goal for Tenkara/fixed line fly fishing for its own sake. On most of the small streams that I fish, the casts are pretty short - by short I mean using a line from several feet shy of the rod's length to a foot beyond the rod's length, plus 2 to 3 feet of tippet. In most cases and I am often using a soft 11 foot long Seriyu rod. I have tried size 2 and 2.5 lines but I seem to always go back to using the size #3 line because it seems to handle the best on the rod I am casting with the size flies that I fish most often (#18 through size 11 dry flies), and I find that I can hold the size 3 line up and off of the water well enough to catch the fish that I am fishing for. But again, I am not casting or fishing very far away and this is on streams that I consider to be fairly open and obstruction free.
On the tighter streams I fish, I am fishing with shorter Keiryu rods (9 and 7' 10" long respectively), with heavier lines to properly load these stiffer rods at much closer casting distances, and I can still hold enough line off of the water to get the desired results in these cramped quarters. But the stiffer Keiryu rods do have the back bone I need to handle the larger occasional fish at close range when sometimes called upon to do that, and I can keep the better sized average stream fish out of the brush, tree roots and rocks a lot better than I can do with my softer Seiryu rod. So I believe a lot of what rod will work out the best for you depends on your individual fishing situations, your individual fishing environments, and the size of the fish that you are catching. It helps a lot to be able to know in advance which rod is best one to take with you where you will be fishing, or have a middle of the road rod that is pretty much OK for just about anywhere that you fish. Realizing, of course, that that rod will be a less than optimum compromise an awful lot of the time.
Most of us have a tendency to gear up for the biggest fish we hope to catch, which really limits our enjoyment with the size fish most of us catch most of the time. And most of those coming from a Western fly fishing background have been conditioned to cast with relatively fast action, stiff rods as being the normal state of their fishing affairs. I liked softer, moderate action western fly rods because light tippets and midge pupa pattern fishing was a big part of my high lake fly fishing success. My first T-rod was a 6:4 action, 12 foot long Iwana rod, and I had trouble hooking fish on it in the beginning. But after a period of adjustment that problem went away. But I do believe many anglers coming to Tenkara fly fishing bring their Western fly fishing rod action preferences a long with them as Chris has noted. Whether there will eventually be an American Tenkara tackle maturing toward the use of softer action fixed line rods remains to be seen. I do dearly love my Seiryu rod and I would fish with it everywhere if I could be effective while using it. But that's just is not possible in many of the places where I fish, so I have other rods that work better on lakes, brushy streams, and for bigger fish under windy conditions with much bigger flies. I think we all have to find our own way through this fishing puzzle and it is probably going to take more than one rod or rod type to cover the wealth of angling opportunities available to most of us, which I don't see as necessarily being a bad thing at all. Having the right tool for the job that needs to be done is one of the joys of fly fishing for me....Golden.