Hand and wrist pain is due to a badly fitted bike, not the style of bars. You can get pain from any kind of bar if you aren't positioned correctly. There are very few bike shops that will take the time to get you set up correctly. Some have trained experts with the proper gear but will charge $100 to $150 for a session. That's peanuts compared to what pro teams spend in wind tunnel time each winter with their new riders and bikes. Any team could spend $100,000 to get their riders measured.
Your hands should be straight, not bent back at the wrist. ie, the palm should be in the same line as your forearm. Bend your wrist all the way back, add shock, repeat over and over and you can schedule carpal tunnel surgery.
When you sit on a bike, you spreading the load on 3 areas: seat, pedals, hands. Dropped bars will tilt you forward putting more weight on your hand and less on your seat. Pedaling harder means less weight on your seat too.
IMO, the worst riding position is straight up right. All your weight is on your seat so riders want a wider seat with more cushion. That means pedaling bow legged to get your legs around the seat which means less pressure on the pedals and more on the seat. That also means the saddle padding is cutting off the blood flow to the legs. Hit a pot hole and all the shock goes straight up your spine.
Runners have a phrase, "dress for the last mile". But too many bike riders seek comfort for the first mile. Those comfort bikes will never get you more than a few miles, let alone 100 miles a day.
Every spring, many riders have to train to get their heart and muscles back in to some sort of shape. Well, you have to get your seat and hands into shape too.
