Thanks for all the responses. It looks like there are a lot of little reasons why they're popular. In my situation, most of those don't apply, so I guess I'm not missing out on anything.
I must say, I don't like the looks of a 3 piece, but the 2 piece bows with the internal riser bolt remain very attractive. I think the 3-piece limb bolts remind me too much of a compound.
Every other year, I do an elk hunt in Colorado, where I pack in about 2 miles to make camp. It might come in handy on that trip to have a nice 2 piece longbow. Besides, it would give me another excuse to buy another one.