Shaft drive has it own problems. Power losses are typically around 15% and they can be heavy and expensive. Plus, they are not 100% problem-free. I managed to snap a U-joint on my BMW shaft drive about 15 years ago and repairs cost me $1200, as it wiped out the inside of the drive housing and the swing arm bearing.
A properly designed and manufactured belt drive, such as HD uses, can last several times as long as even an O-ring chain. Maintenance is minimal. All you have to do is stay away from gravel roads and check the belt tension every 10K miles, or so. They rarely need to be re-tensioned, though. However, the cost to manufacture a belt system is more than a chain drive. Like shaft drive, changing gear ratios is almost impossible for the owner and replacement belts are expensive and can usually only be purchased from the bike manufacturer ($$$).
Personally, given a choice, I would prefer a belt drive for street riding. I like the light weight, quiet running, lack of maintenance and cleanliness.