Also...that unrestrictive tube you mention, the air intake snorkel, is actually pretty small. It does bring in "cold" air from in front of the engine bay, but the volume is not all that great.
As for my mustang on the dyno...yeah, sitting still was not all that great, but...the hood was open too, so the under hood temps were not all that great. The open filter was exposed to cooler air coming in from the top.
I do think the filter box mod is good...if done right. I removed the snorkel tube, drilled the holes in the box, but did not drill holes on the back side towards the engine. I kept the holes in the bottom and front sides of the box. My box is still getting most of its air from the front side where the snorkel was.
As you said, hot air is less dense and not good, but the restricted air inlet is not good either. I think the holy box is a good compromise...if done right. An open filter can be used with great effect (just look at the Ford Lightning pickups) but in not necessary in out case with out limited power.
I have not seen dyno results on an Explorer either, so I can't compare.
I did dyno my stang with a large, open K&N filter...and again with a fender mounted cold air setup. I got results within 2 hp of each other every time.
Ken