Regarding negative attitudes about Tenkara, maybe not so much now, but there was a time not too long ago many "sportsmen" felt the same way about fly fishing in general - Someone in rubber pants swishing around a long floppy rod.
A lot of those perceptions may have changed when "the movie" came out, and it became somewhat hip.
I'm the first to say, fishing a fixed-length line (tenkara) is NOT for everybody. To directly answer your question of what folks will enjoy tenkara, if I use the basic progression many fisher folks go thru -
Wants to catch first fish - Yep
Wants to catch alot of fish - Yep
Wants to catch the biggest fish - Nope
Wants to catch difficult fish - Yep
If you are going to loose sleep when you break off the biggest fish of the month, you are better off sticking with snake guides.
Regarding size of fish you can expect to reasonably catch, trout up to 16 - 17" are doable. After that, your chances go down. The system is design to accurately, precisely, and delicately deliver and present your fly. That is at the direct expense have having the brute strength to literally stop a large, fresh fish dead in it's tracks. Unfortunately as of yet, we can't have it all. Of course, that's why they make reeled rods in 1 weights and 12 weights.
It's sort of interesting, if you look at the folks who take up tenkara, I don't think it's a bell shaped curve when it comes to experience levels. I think you see a big blip with folks who haven't fished (or fly fished) much, an another blip with folks who have been fishing along time and have gotten past being enamored with equipment (not to say being enamored with equipment isn't fun).
Hope that helps a bit. And please feel free to ask any other questions you may have, this is a great place to get them answered from a variety of perspectives.
p.s. If big fish are the target, there are fixed-length line rods designed for that purpose, they are called hera rods. The thing is you give up the delicacy/precision for which tenkara rods are designed. Of course even the hera rods have a limit, you hook a big enough fresh fish and try to literally jerk it out of the water, something is going to give.
p.p.s. This looks like a great option for large fish -