A big reason is that you don't have quick or ready access to your brakes -- and when you need your stoppers, you usually need 'em badly ;-) Even the specialized time trial bikes that the pro rides and some triathlon folks use have the brake levers on the regular handlebars, not on the aerobars.
A lot of my female friends here buy and install aerobars on their bikes to help them cheat the wind...
Aerobars are specialty tools for special types of riding -- specifically to let you go as fast as possible in as straight a line as possible. Your balance on the aerobars as well as the way your bike steers is way different than if you're riding on the regular drops. In group rides, you need to have quick reaction and control of your bike in order to react to the actions of the riders around you, and you simply don't have that when you're on aerobars. Yes, pro riders do it in team time trials, but few of us mere mortals put in the practice that they do...
Tom




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