I think the OP is asking more along the lines of how long the engine might last if just idling, rather than the car itself- hence the assumption of an unlimited supply of fuel.
Now, if you simply parked a brand-new, modern electronically fuel-injected car next to a massive storage tank of gasoline, connected a small hose to keep the car’s tank full, and just left it to idle, that car could very likely idle for decades.
It’s first failure would likely be external to the engine- as noted, perhaps the alternator or AC compressor fails, or one of the sensors. It’s first internal failure would likely be a relatively minor ancillary part, like the water pump. (Either of which might last the equivalent of 100,000 to 150,000 miles.)
A modern EFI car with an oxygen sensor and such, would greatly minimize oil fouling (since the A/F ratio would be kept near-perfect) and deposit buildup.
Up on the North Slope, the oil companies have fleets of diesel trucks that, in some cases, have been running constantly save for an occasional oil change, for years. And that’s running and being used, so the car, if just idling, would last… well, probably a lot longer than you want to wait around and watch.
Now, if you did a sort of labratory experiment, and put the same new car engine on a test stand, and connected it to external coolant and fuel, removed as many external accessories as possible (smog pump, water pump, etc) could swap out any sensor that fails, as it’s running, and used an external oil sump so the oil could be carefully filtered and changed, also while the engine is still running, that engine could, concievably, run essentially forever.
With a pressurized oiling system, the only true metal-to-metal contact is the occasional piston-ring-to-cylinder-wall contact, and even then usually only at peak cylinder pressure. The rest of the time, nearly everything is running in an oil-bath, and there’s basically no actual contact between moving parts.
That’s not to say parts won’t fatigue eventually, but assuming the OP’s “just idling”, that minimizes the strain- parts designed to withstand sustained 8,000 RPM doing a mere 700 rpm, etc. Basically you’ll be waiting for a small part to fail first- a clogged injector, a valve spring breaking, etc.
To answer the OP: Given unlimited fuel and good conditions, yes, that SUV could easily idle for several years.