I don't recommend modifying the airbox door or running without it; any airflow gains aren't consistent due to turbulence as well as water ingress and other crap.
The proper way to increase airflow (after the snorkle-ectomy) is to do the "L-Mod" or cut 4 - 1" holes in top of the airbox (which doesn't allow any more water, etc. in). Make sure it's limited to the clean side!
I hope your bike is jetted properly for the increased airflow! 22 cent mod if you must, but the KLX kit from Eagle Mfg & Eng
is the best solution. Follow the directions. Don't know? time to pull the carb and check; be careful with the plastic enricher nut (brass/alum replacement is available from Stead Engineering) and the carb diaphram.
....and lastly, here's more than you ever wanted to know about the KLR airbox, courtesy of the late, great, KLR guru Cary Aspy (KLRCary)
A lot of missunderstanding with airbox issues.
First, the screen. Airflow gains are not linear. Removing the screen with an otherwise stock KLR airbox will only gain you 2 cfm. The engine won't know the differance. However, with a heavily modified airbox, the gain from removing the screen is 8 cfm. Depending on what else is done to the engine, you may make more power. I doubt that you'll feel it, but a dyno will show it. Butt-dyno's can detect very small low rpm changes, but don't detect higher rpm changes very well at all. You'll likely not detect it, but that does not mean it's not there.
Comparing screen removal to other models is wrong, particularly with the newer sportbikes. With them, the screen often serves another purpose as well. Air distribution in a 4 cyl sportbike can be a real problem, particularly with "ram air". Removing the screen on them can cause very real losses, depending on the model. That does NOT apply to the KLR.
Same thing with air filters. There is only about 2 cfm differance from the best filter (UNI), to the worst (K&N). With a modified airbox, that differance grows to 9 cfm.
Here is the flow chart:
Completely stock - 64.8cfm
Same - Remove snorkle - 74cfm
Same - With UNI filter - 76.2cfm
Same - Remove screen - 78.6cfm
Same - Small "L" cut - 85.1cfm
Same - Large "L" cut, open snorkle area further - 92.4
Same - Remove door - 103.2
Alternate - UNI filter, No snorkle, With screen, No door, No "L" cut - 95.4
All at 2" of water, tested at 1 1/2" and 3" and averaged to 2"
To answer the larger question, how much air can the KLR really use?
A stock KLR about 70-80cfm. With a good pipe about 75-90cfm. A modified motor about 90-100cfm. Having a bit more capacity than you you need will not hurt anything. The effects are not linear though. Going from 65cfm to 75cfm you will likely notice, but going from 75 to 85 cfm you likely won't.
Part of the confusion might be due to the effects of the carb shimming. Since that mod is for a stock needle, the snorkle removal serves not just to add air, but to lean out the top end. The stock KLR till 07 is rich on the top. ( The 08 has a smaller main jet.) Airbox mods have much more effect on top end mixture, so, with the stock needle it also helps straighten out the fuel curve.
Finally the airbox door. You've got to carefull there. You don't have clean air there. It's flowing past that door when riding. You can easily create a partial low pressure area there, depending on wind direction, and where you place your leg!
I do not recommend removing the backfire screen (PITA) or running without the airbox door for reasons that should be obvious.
Though a KLR isn't going to have a bunch more power no matter what you do, a KLX kit combined with the snorkle-ectomy and L mod or 4 - 1" holes will have it running properly. don't bother with the little 1" foam filters if you drill the holes - they are useless.