"For the local truck eating bridges often times it's the rear end/trailer that gets caught. The drivers know how tall their cab is but forget that without a load their trailer is a little higher than normal. And sometimes the new trailer is taller than what they had ran with before."
I get that the trailer hits the bridge, but if that happens, it's the front end of the trailer that hits the bridge, so letting air out of the trailer tires (which are on the back end of the trailer) would lower the back end of the trailer, where it's the front end of the trailer that's stuck. Unless you deflate the drive wheels of the tractor, the part that's stuck won't settle. In fact, in the first picture of the first link, deflating the trailer tires would make the problem worse as the trailer levered up on the kingpin, driving the leading edge upward even harder into the bridgework.
I did notice that there was one picture where the "deflate the tires" trick would work very nicely. There was a picture of a wheel-loader on a flatbed that was just barely wedged, and since the wheel-loader's tires have about a twelve inch sidewall, deflating the tires on the wheel-loader would have freed it very easily. The flatbed looks broken across the lead trailer axle so I'm guessing that the trucker couldn't have done that and then driven off, but at least he could have lowered the wheel-loader and then dragged the trailer out in the open to be re-lynched or replaced.