I'm more on the loathe side. I have a couple that I wear occasionally, but it's never been my best look.
For me, I think it's that it's hard to find a length that doesn't cut across me in a place that emphasizes where I'm widest, as many of them come down to my low hip, creating a horizontal like right at my saddlebags. I think the point about emphasizing the legs is exactly why tunics don't work well for me.
Tunics also tend to hide my waist, making me look like everything is as big as my boobs and my hips. Not a great look. Also, they're not an easy fit for me -- tunics usually catch on my hips instead of skimming and falling loose like they do on slimmer-hipped women. When I size up to accommodate hips, the waist and shoulders are often too big. So fit is an issue.
A good tunic for me needs to have the right combination of drape but some heft as well -- and it needs to be slippery like silk so it doesn't catch and cling on my hips and butt. I don't always pay close attention to the rear view, but I've learned that long (especially knit) tunic lengths don't tend to flatter my rear view.
I think that a print can help a tunic style for me -- just as printed dresses usually look better on me than solids. Prints hide lumpage and bumpage and keep the eye moving around.