Micro fishing line is line geared to the size of the fish. There is no point fishing for two inch fish with four pound test line. The flies or baits used are so small, and the hooks are so small that anything other than a very thin line is going to look like a rope in comparison.
I have read that in the Edo period in Japan, the line used for tanago fishing was a single human hair, "preferably taken from a woman you love." Over there and back then, women wore their hair quite long. I don't think many of us in the here and now would be able to do much fishing if we had to use a single human hair. And although I have fished with a single horsehair and caught fairly nice fish doing it, horsehair is much too thick for this type of fishing.
The line that is used to snell tanago hooks is just over 1 pound test. Of course, there's not a tanago alive that weighs even close to 1 pound. Similarly, the fish that people here target when micro fishing are very small - a few inches - and their weight is more appropriately measured in grams than ounces - let alone pounds. The lines that have been used for microfishing, 4# test or even 2# test, seem like overkill. I say give the micros a fighting chance.
However, and this is a big however, I have both read and heard about instances when an angler fishing for a 3" fish catches a 9 or 10" fish, or hooks a fish more properly measured in pounds than inches. If you are fishing with line that breaks at 5 ounces, it will break. You just want it to break near the hook so you don't lose your whole rig.
These micro fishing lines should perhaps more accurately be called micro fishing tippet. Your float, if you use one, should be on a stronger line. They're just expensive enough that you don't want to lose them if you don't have to. Similarly, if you will be fly fishing for micros, you'll need a slightly heavier line to be able to cast (after all tanago fishing is not just dapping). However, the line you'll need is still almost unbelievably light.
For micro fishing, I would highly recommend a very light tippet. If you happen to hook a 9" brookie when fishing for a 3" dace, which has been known to happen, you might be able to land it if you play it skillfully. However, if you happen to hook a 4# carp when fishing for young of the year bluegills, which has also happened, you wouldn't have a chance of landing the fish but you would save your rod!
And if you don't agree that micros should be given a fighting chance, and wish to use a stronger line, I do have the Varivas Super Tippet in 7X, which has a breaking strength of 2.4# test; 8X, which has a breaking strength of 1.8# and 9x, which has a breaking strength of 1.6lb. The 10X is now available only in fluorocarbon. That way, you can fish the shallows for the dace and the pools for the brookies without having to change your tippet. (The button has choices for thicker tippets, but for microfishing I would choose the thinner ones.)
There is a lot we can learn from what they do in Japan. I'm not sure how much we can learn from what they don't do. There are significant cultural differences. Building a better box is something they are very, very good at. Thinking outside the box, not so much. That the Japanese don't use flies with 6' rods for 3" fish, in all seriousness, might be because it has never even occurred to anyone.
It does work, though, depending on the fish you are after and your degree of stealth. I have caught trout, largemouth bass and bluegills on flies with a 6'6" rod.
The Suntech Kurenai HM30R, the Nissin Air Stage 190 and 240, or the Suntech TenkaraBum Traveler 27 will all cast a light tenkara line quite well. For fishing with the smaller flies you will use for smaller fish, I would recommend the Nissin Oni Tenkara size 2.5 line.
The Kid's Kit rod will work for micros also. The size 4 line included in the kit is easy for a child to learn to cast, but is really too heavy for micros. I would still suggest the Oni Tenkara size 2.5 line if you intend to fly fish for micros, even though it may take more time and more practice to cast it well.