I've got some experience with both the weedy version and the cultivated stuff.
weed: nutsedge is a pretty incredible plant. the "nuts" are really small, but have a pleasant taste. the plants are small, but I've seen roots from a single plant run at least five feet horizontally in loose soil. the plants are relatively easy to remove, but the nuts are not, which accounts for the difficulty getting rid of it. could easily replace a lawn.
chufa: bought 1/4 pound of tubers a few years back. they're probably five times the size of the wild weedy tubers. been growing it in gallon pots since then. goes in the greenhouse over the winter, since it wouldn't be cold hardy here. it hasn't really been thriving, but it's limping along. should I ever get a larger greenhouse built, I think chufa will stay in there permanently. horchata is roughly the best thing ever, but I haven't harvested any of the nuts yet in the interest of expanding my stock. much less vigorous than the weedy stuff. where I'm at, making a lawn out of this stuff would not work, but that might be an option someplace warmer. chufa does like to stay wet, so it would do well in a soggy spot.
not a lot of information, but I hope it's at least mildly helpful.
I'm abit confused why are people treating them as long-term annuals or perennials? The plant did originate as an annual but according to A History of World Agriculture it was a crop in short rotation during and after the flooding period of the Nile.
Eatyourgreens channel on youtube grow it as a short crop and so does a farm in Quebec (90 days)
I could easily see there being a benefit to a longer season but after a while wouldn't return diminish?