Not easy to explain so if the following sounds like gibberish (which it probably is) apologies.
When your engine is running and on the intake stroke the fuel / air mix is rushing in through the inlet port at very high speed. Most of this mix passes in to the engine and gets ignited. However, some of this fast moving vapour doesn't make it in to the combustion chamber before the valve closes, hits the valve at high speed and bounces back - potentially back through carb and out in to the atmosphere. You can see this really easily on a piston port 2 stroke that is in a high state of tune - they can literally spit petrol straight back out; it's the same thing happening on a 4 stroke.
Now this vapour could be lost to the atmosphere (as I said above) or, ideally, 'trapped' and drawn back in to the engine for another go on the next intake stroke. This 'trapping' is done by the bellmouth design on the carb. The original airbox usually has a good design and cheap pods don't. You can get all sorts of swirl effect etc with poor designs and an inconsistent supply of this vapour - hence a cough every now and then for example. So sometimes your bike will fire with a weak mixture, sometimes it will be fine. Crosswinds can play havoc with this as well.
So the weak mixture that you get when you pull the airbox off is not only because you have an unhindered supply of air (no filter getting in the way) but you are also losing fuel vapour out of the back of the carbs.
When your engine is running and on the intake stroke the fuel / air mix is rushing in through the inlet port at very high speed. Most of this mix passes in to the engine and gets ignited. However, some of this fast moving vapour doesn't make it in to the combustion chamber before the valve closes, hits the valve at high speed and bounces back - potentially back through carb and out in to the atmosphere. You can see this really easily on a piston port 2 stroke that is in a high state of tune - they can literally spit petrol straight back out; it's the same thing happening on a 4 stroke.
Now this vapour could be lost to the atmosphere (as I said above) or, ideally, 'trapped' and drawn back in to the engine for another go on the next intake stroke. This 'trapping' is done by the bellmouth design on the carb. The original airbox usually has a good design and cheap pods don't. You can get all sorts of swirl effect etc with poor designs and an inconsistent supply of this vapour - hence a cough every now and then for example. So sometimes your bike will fire with a weak mixture, sometimes it will be fine. Crosswinds can play havoc with this as well.
So the weak mixture that you get when you pull the airbox off is not only because you have an unhindered supply of air (no filter getting in the way) but you are also losing fuel vapour out of the back of the carbs.