The simple answer is that they are attached to the aerobars. I think you mean why aren't they on the extensions with the shifters. Aerobars are usually set up this way: A bar is attached to the stem; this bar is either flat on top or a round bar like typical road bars. Instead of having drop bars curving down like a typiical road bike it curves forward and generally a bit up at the ends. The brake levers attach to the end of the bars. Your extensions with armrests are either an integrated part of the bars or an attachment. The shift levers are at the end of these extensions. Now, I suppose someone could design a brake/shift system for the extension ends but I see a couple of problems with it. First, if you have to brake it is safer to have your hands at the furthest extent to the side for stability. Why are you braking in a TT? Usually on corners or downhills where control is paramount. Second, I would guess from an aero perspective, having this kind of shifter on the extensions may be slightly "dirty" compared to the current setups. Finally, as most people in TT position have their hands wrapped around the shift levers or right behind them, it is easier to shift with your finger than taking your hands off the bar to push a lever (in road bike position, hands on hoods is easy to push the levers in).
With the advent of electronic shifting, I could see doing away with the shift levers on the extensions and moving the brake levers there (although again you want greater stability when braking) and using buttons for electronic shifting.
HED has a third break system in which you have an adaptor that puts the third break lever at the extensions for the rear break. I will say, not needed.
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Thanks for the help. I am still getting use to the bars, and I see your points in a solo race scenario as they were designed for.
It still seems potentially useful in a practice scenario, where the roads aren't closed and things happen. Thanks for the input though, I appreciate it.
One more reason: physics. When you brake, you keep going forward while your wheels are slowing down. That creates a torque that could flip you over the handlebars, and the best way to avoid this is to keep your center of mass back. In aero position your center of mass is too far forward, so if you applied much braking force you'd go right over. If you pay attention while braking, you'll notice that you move back on the seat naturally, which you can't do in the bars. I haven't seen this HED 3rd brake system, but braking with the rear wheel creates much less torque, although it's also less effective at slowing you down.
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