The DOHC carbs are a CV design. CV means Constant Vacuum. As part of the design, the carbs need a certain amount of vacuum/low pressure on the intake side to work correctly. The stock airbox was specifically designed to supply this. Removing the airbox disturbs the carbs enough to cause the off idle condition you mention, and some other stuff I'm sure you've experienced. I've read a few stories of using a lower restriction air filter inside the stock airbox causing this, but that may be a corner case for that particular bike.
Me personally, I've been a form-follows-function kind of guy. In most instances, I couldn't care less how something looks, as long as it operates correctly. I can always make it look pretty later, but it's GOT TO WORK FIRST. That's just me and my big ole opinion.
Luke M
Used to have a 1979 CB750L, sold it as a parts bike, now riding a slightly modified 1984 VT700C. Network/Field Engineer. Central OH, USA, Earth, Sol System, Milky Way Galaxy, Universe.