I do not get the futile War on Henbit/Dead Nettle.  Futile wars are many and varied, and in the overall scheme of things the futile War on Henbit/Dead Nettle is small potatoes. But at least I can be pretty sure of the righteousness of my high dudgeon in this futile war. I’ve lived with both henbit and dead nettle for many years. We have lots of turf at the Hungry Holler (6 acres). We mow more of it than sane people would. If I had my way, we wouldn’t have so much grass, but we do. We live intimately with it in all seasons. 
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A perfectly manicured lawn gives me the creeps. It’s not natural. A dandelion-free yard takes all kinds of ‘cides, herb and pest; and fertilizers and unhealthy obsession. I know something about unhealthy obsessions too, but that’s for another rant. 
The point is, henbit and dead nettle are dang pretty in the early spring. At the Holler it’s the first color after a drab winter. Bees are happy to see it. It’s slim pickens and they’re hungry. When I go out to admire the purple, I can hear it before I see it. The bees are feasting. 
Once you start mowing in earnest, and as turf resurrects around Easter, you’ll soon never know henbit was even there. So get over it. For everything there is a season.