The airbox is a very good noise reducer. It also provides "static air" for the carbs to draw air from. It is a pretty good lower front part of the rear fender until it begins to crack from age. It is a good place to mount fuses, relays, etc. until the rubber mounting straps break. It is a good battery box.
However, it really robs the bike of POWER, IMHO. Mine runs better from idle to redline without the airbox. It starts better, idles better, and really pulls above 5500 rpm.  I haven't touched the carbs in 20000 miles except to check carb balance a couple of times--no adjustment needed. I get 50+ mpg, and I do not ride like a grown-up. 
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Larry
2003 T-100 (790cc), NARK, NH Togas, 8100 rpm rev limiter, 158 main jets, 42 pilot jets (less than 1 turn out on pilot screws), stock needles--no shims. 13 A/F ratio from 1100 rpm to 4000 rpm; 12 A/F ratio from 4000 rpm to 6000 rpm; 13 A/F from 6000 rpm to 8100 rpm.:D
2007 Tiger 1050--White:D--SW-Motech crashbars, Skidmarx rear hugger/chain guard, Calsci +7 windscreen.
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