There's cultural impacts - most bikes on the North American market specifically built for touring include drop bars. Go to Europe, and flat bars are much more common.

From a functionality perspective, multiple hand positions is a big deal on long rides - even people I know that tour on flats always add bar ends to add some variety. Flat bars also force an awkward twist in your forearms that can get uncomfortable on a long ride. The widely spread grips on flats make you more stable, but it also creates work for your shoulder muscles - because your hands are wider than your shoulders, any weight supported on your hands requires more shoulder work than on a narrower spread.

Trekking bars are pretty much never available on a stock bike, but they're also a popular option for touring, and provide much the same benefits as drops.

My bike came with drops, and now that I am used to them, I don't think I could go back. I rarely use the lower hand position, and my bars are higher than on many road bikes, giving me a seating position that's more upright. All in all, it's quite comfortable.