I own one, and have used exhaust jacks before. Here is the only pic I have of one in action (lying muddy to the side):
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Yes, one will relatively easily lift a stuck SUV. It’s a solution that works well in some situations.
A drawback in my experience, is that it’s difficult to keep the filler hose seated on the tailpipe, requiring constant pressure. Though once the “jack” is filled with gas, it stays inflated.
As to concerns on stability, I challenge you to find a stable lifting solution that works well in the mud. The HiLift is the best alternative, and those are unstable by design. And no, a bottle jack does not work in these situations.
If I regularly wheeled in heavily swamped areas, like some friends do back in Russia, I would likely carry one. I don’t really see a need for one elsewhere, and I don’t carry one anymore.