Variance is more a measure of the frequency of swings (wins vs losses), not just the size of them. At any given stake and volume, the size of LHE swings will be smaller because the pots are smaller, so the risk of ruin is generally less. That may be what you're confusing with "lower variance." But the wins are also smaller for the same reason, and typically fewer in number because you're getting to the river and showdown more often than in NLHE. So the swings are smaller but typically much more frequent, ergo the variance is higher.
With NLHE skill/style adds more to your edge because the better player very often wins with the worst hand by not letting you get to showdown. Also, better players will often fold worse made hands without building a big pot when a worse player with a better hand spazzes out and prices him out of the pot. Fold equity is a huge element in NLHE strategy, but barely exists at all in LHE. The edges in LHE are smaller because so many more hands go to showdown due to people being priced in to call with more draws and speculative hands. It's not just about bad players not folding, although there is that too. But certain plays are 100% correct in LHE that are lolbad in NLHE because you're getting a price.
That's not to say there are no fish and that you can't be profitable, nor is it true that it's only for small bankrolls. Compared to NLHE it's just not as exciting or *potentially* profitable, again because of the small pots and swings. For risk-averse players who don't thrive on the thrill that NLHE players get from big-pot/all-in/bluff situations, LHE or the other limit games seem more like "pure" poker.
LHE is also considered "solved" by computers and bots, while NLHE is not. While some argue that NLHE can never be truly solved, I expect one day there will be enough computing power to approximate the human brain in such a way as to minimize mistakes to the point of beating 99.9% of human players.