A driver eating cereal while driving down the highway. Full-on bowl and spoon action trying not to spill milk on himself while commuting.
On several levels the risk/reward just doesn't add up.
In cooler weather I throw a couple of blankets on top of the mesh bikini under the soft top and it does wonders for both quiet and warmth.
I normally keep blankets in my vehicles anyway and this approach effectively takes up zero space. It's a win all around.
As to the cause/effect mentioned in the thread title, the door seals help maintain the vehicle's vacuum pressure. With the doors off, all that vacuum is lost.
It doesn't happen if you park with the windows down or when the top is removed because the truck's computer doesn't monitor the state...
Turn on the big air compressor and break out some breakdance-size pieces of cardboard. Dress in old clothes, lay the cardboard down under the truck, protect your face, and get to spraying everything that's not the exhaust.
Honestly, that's pretty much the deal. For nooks, crannies, and tiny...
I've been annually coating everything in a lanolin based rust prevention treatment. (Fluid Film, Wool Wax, Corrosion Free, etc.). It makes a huge difference.
I recently tried Blaster Surface Shield and it's my current favorite. It's also pretty affordable when bought by the 5 gallon tub. If...
I spent money.
Ordered a set of Bilstein 6112s last night. Stage 3 Motorsports currently has them at the best price I've ever seen:
https://www.stage3motorsports.com/21bronc4d6112-21-22-bronco-4-door-sasquatch-bilstein-b8-6112-suspension-kit.html