Well, personally, I do think bindweed is pretty, but its out of control around here. There's no way to keep it from strangling other crops other than ripping it out repeatedly, it invades with horrifying quickness, and I simply don't have the time to harvest the massive amounts of seed my total amount of bindweed produces. In fact, I have so much of it that I'm considering buying or making a composter just to
compost bindweed without risking it spreading even more enthusiastically.
If I could ever get it to stay put, I'd be happy to leave some. <laugh> I'm never going to eradicate it, but I do hope to reclaim some areas from it.
If harvesting works for you, best of luck.