I'm pretty sure that spare tire is only there for the joke. With off roading tires that large they are almost definitely bead lock tires which can be ran at very low PSI without risk of the tire departing the rim. On top of that the tread is much thicker meaning punctures have to go deeper before they cause problems and most of the time came be fixed by simple plugs.

Not to mention the logistics of changing a spare on a tire of that size. A bottle jack is completely out of the question and you wouldn't be able to use a farm jack safety with the body that high. Even if you could how are you going to get that wheel onto the studs when it weighs over 300Lb?