Don't simply remove the snorkel and let the engine breathe hot air. Hot air costs power, probably as much as you gain (if, big IF, you gain anything) by removing the snorkel. If you remove it, replace it with something that flows better and brings in cooler air. On an NA engine, you loose a handful of HP for every 10 degrees above 90F the air gets.
I have not flow benched an NA IDI air filter or snorkel, but I did do the system on my F150 5.4L for an article and have done about 10 other systems over the years with similar results. On my F150, the stock system flowed way more than the engine needed in stock tune but the biggest restriction was the filter element itself. One of the more popular shadetree modifications to the 5.4L intake was also tested on the flow bench and it made very little difference in airflow. Going to an aftermarket intake made a big difference in airflow but didn't make a huge difference in power output to an otherwise stock engine when tested on a dyno. The equation changes when you increase the power output by other means, (new tune, head work, pump mods, exhaust mods, etc.), which then increases airflow requirements, and the stock system may not have enough airflow capability me meet those demands and it begins to restrict power. On an otherwise stock engine, intake mods seldom add much power unless the stock system was really poorly designed (often true in the olds days, less true today). I've seen it many times on the dyno, testing free-flow filters and intake systems on stock trucks. On a chassis dyno, any gains are pretty hard to find over the normal noise and inaccuracies and if they're there at all, they are in the upper rpm range. Have seen more and better results more on engine dyno, where you can reliably see and reproduce a 5 hp gain. For most trucks and chassis dynos, my opinion is the margin for testing error is 10 hp plus or minus and I don't go dancing for joy if any gains show up under that margin. Especially if they can't be almost exactly repeated a MINIMUM of three times. In other words, don't hold up any chassis dyno testing you see as gospel unless you KNOW the test methodology. Anything recent I've ever mentioned or written about meets that standard.
The moral here is that once an engine has enough airflow to match the power output, giving it the POTENTIAL for more doesn't increase power. It needs what it needs at a particular power level, plus a little extra to account for air filter restriction due to dirt loading. This holds true all the way thru the rpm range. Restriction will cost more power at the upper rpm range. From the OE persecutive, they know most people aren't going to run their 6.9L at 3300 very often, so if the filter is restrictive from 2800 to 3300, they don't care much if the more restrictive (and quieter) system is less expensive to produce and easier to fit under the hood.
You can test this at home with a restriction gauge. Google Filter Minder. It a relatively inexpensive device (basically a recording vacuum gauge) that measures and records intake restriction. It's designed to tell you the best time to replace an air filter (which should be based on restriction, not some arbitrary mileage number). Install one with the widest range of numbers, 5-25 inches of mercury would be a good choice, or 5-20. Install it along with a new air filter and do some WOT runs up to redline. Observe the recorded restriction. If it's 10 inches or less, you gain very little by spending a lot of money to bring it down. If it's above 10 and you want to play, make whatever changes you think appropriate, reset the gauge and try again, working towards getting it as low as possible or as low as possible for the amount of money you want to spend. If it's a lot over 10, you are pretty much guaranteed a power boost by bringing it down. Start with the easy stuff... the filter element. I have discovered, for example, that certain low-rent, no-name air filters are highly restrictive versus an OE replacement or a good brand name. I know some of you have orange, but FRAM is at the forefront of air filters and makes some nice air filter elements.
FYI, on my Gen 1 Banks turbo system, complete with a K&N air filter (I do not like oiled cotton gauze for a filtering efficiency standpoint, but there is no drop in alternative), my engine will generate about 14 inches of restriction at redline, full-load power with a perfectly clean filter, or with the filter element removed. That shows me whatever restriction there is in the housing not the element. That restriction comes with a boost pressure of around 12-14 (a little higher than 10 10 psi Banks avertized), a fairly mild fuel rate setting on what amounts to a turbo-spec pump and a 4-inch exhaust (which will be replaced by a 3-inch when I can because it doesn't make more power, just more noise).
One thing specific to our engines, unlike electronically controlled diesels (and EFI gassers) which can change fuel delivery to suit available airflow, the mechanically injected engine is numb to airflow. It squirts a preset amount of fuel no matter what and responds to only two inputs, RPM and the position of the foot feed(maybe fuel inlet pressure too but it's not really designed for that to be an "input"). If there isn't enough air for that fuel.. the pump says "tough maracas" continues along the same path and the engine simply blows smoke and loses power. So, if any engine responds well to a reduction of intake restriction, it would be ours, but it remains to be proven to me what exactly works and is beneficial. I am largely skeptical because in the cases where I have tested "common knowledge," especially when it come to shadetree mods, I was usually underwhelmed with the results when the mod was tested objectively. But, you never know and I keep an open mind.