Cue the Jaws movie theme music.
Landing larger fish may present a challenge, but I personally think the challenge is what makes fishing fun. The one thing I like about Tenkara, I think it will make you a better fisher person. This is particularly true in the process of trying to control (and hopefully land) larger fish. The challenge is certainly there, but I think in most cases, all the odds aren't on the side of the fish.
There are alot of real nice conventional fly reels on the market today, and that has become a mixed blessing. It allows the conventional fly angler let the disk drag reel do the work in subduing larger fish. The angler strikes the "orvis pose" (rod high over head) and hangs on. When the fish runs, the reel supplies resistance (and about a mile of line), when the fish gets tired, the angler derricks in the prize.
The one thing to remember when fighting fish, the fish always follows his/her head. The fish can only go where it's head is pointing. A fish's head does not move up and down, so when you apply overhead pressure, it needs to be sufficient to lift the fish out of the water column, if not, it doesn't do much good. The fish feels pressure and responds by heading in the opposite direction. That's exactly what you don't want to happen in Tenkara. (It isn't all that great with conventional fly gear either, but that's where our old friend, Mr Fly reel comes in with several hundred yards of line and a disk drag that can slow down a Buick Park Avenue.)
A fish's head is made to move side to side. When a fish's head is side loaded, it has one of two choices, either follow the direction it's head is being pulled, or expend alot of energy trying to pull it's head in the opposite direction. Of course, things can get even more complicated for poor old Mr./Mrs. fish when that direction of pull suddenly changes from one side to the other. Once the fish starts getting turned, he/she must now also fight any current, which will tend to try to further spin the fish. (When pulling straight up and back on the fish, it takes off straight down steam, so the current is working in the fishes favor).
Tenkara equipment excels at providing side pressure to the fish, and with the mere flip of the angler's wrist, suddenly that point of pressure moves 24' in the opposite direction from where it was just a second ago. Bottom line, in my opinion, Tenkara equipment can be a very effective fish fighting tool.
Of course, everything sounds easy in principle, and things don't always go exactly as planned. But that's what makes it fun, and trying different things is what makes one a versatile angler.