The LHT is a heavy somewhat unresponsive touring frame that I liken to Grandpa's old Buick. Some like them, some with valid reasons, some are just lemmings.
IMHO a cross bike is the perfect compromise bike for commuting. Can still carry a load, takes larger tires and fenders, for the most part is the perfect marriage between the speed and handling of a road bike and the durability of a tourer.
And you're not even required to have to put a Brooks saddle on it like you would with a LHT
I have a Fuji Cross Pro, and a Salsa Vaya which is more an offroad tourer than a cross bike. I love them both, but the Fuji remains the "go to" bike for commuting.