If you're going to go touring self-supported, I'd recommend a touring bike. On tour it's you and your bike against the world. You want something that does that. If you buy a tourer for touring, you can use it for other things and it's not bad. I have an LHT. Yes, it's heavier than my road bike - especially with the very-strong front and rear racks, the fenders, the sprung Brooks saddle, and of course, the spare spokes mounted on the chainstays. When I pick it up after being used to my road bike, it does appear to weigh 700 pounds. But when I'm out touring, I'm so happy to have it.
I've ridden it on day rides and centuries. It's not great for those, but it's fine. If I was going on a long, self-supported tour and could only afford one bike, I'd be happy to have an LHT, and I wouldn't complain about its weight when I was riding a century.
HOWEVER, if you're not going to take a long, self-supported tour, I think buying a tourer like the LHT wouldn't make sense. If you really want a bike that can ride on both roads and dirt, do both fairly well, and you don't want to tour, a cyclocross bike might be the ticket.
Actually, I think the real answer is to have a different bike for every type of riding you are likely to do.