Because Korea is extremely dense and that makes it easy to essentially 100% cover with cell phone service. The Grand Canyon has a vast wilderness, almost comparable to Siberia.
Whether a car sat-nav makes sense depends on the unit
A traditional Sat-Nav device (you mis-call them "GPS") has a huge amount of memory to store pre-programmed maps of your region. It also has a GPS receiver so it knows its coordinates.
However, obviously, the trend is to go to "cellular data connected" types, because they have the latest maps, do smarter routings based on collected data, and are able to adapt to live and past-pattern traffic conditions. These will be useless in many parts of the Canyon.
Increasingly, the car rental agencies are likely to hand you a loose "device" that is basically an Android tablet, and rent that to you for some outlandish price. Don't count on it being mounted, integrated, or audible in driving conditions.
It also depends on the language.
Where's your brain-trust?
"Who is your English speaker?" vs "Who is your driver"?
Because the rental-car company supplied unit will be English language, almost certainly. If only the driver speaks English well, this is a bad division of labor. The rental company's choice of device will be unfamiliar and awkward. To be clear, the person driving is not the person who should be dealing with the nav. Messing with any smart device while driving is always dangerous; but an unfamiliar or balky one is much more dangerous because of how the brain responds to unexpected behavior. Brains do not multi-task; they rapidly task-switch (badly). Unexpected behavior from a balky device makes the brain not switch back at the expected time, extending the head-down time and making you crash.
If there are 2 adults in the car, the driver should not be navigating or interacting with electronic equipment. The other person should. Which means the nav aids need to be in that person's language.
Which brings us to the ideal division of labor on a long road trip.
Driver drives. Navigator navigates. Navigator is always right.
The best division of labor on a road trip is 2 people: One person to drive and the other to navigate. The driver treats the navigator's word as absolutely correct. If the driver strongly feels otherwise, the driver pulls over safely to the side of the road and they look at the maps together and resolve it. *The driver does not badger or argue with the navigator, or make the navigator afraid to speak freely. The navigator does not give too-late or shaky/uncertain instructions; better to give a wrong instruction firmly, then at an appropriate time, a second instruction to correct the course**. Once you get the rhythm of it, it works very well.
Obviously, that creates a language dependency.
A sat-nav attempts to automate the navigator's job. A human navigator is worlds better. The human might use the sat-nav as a tool, but would be better off using tools the navigator is already familiar with. I certainly would be reluctant to reserve in advance a Sat-nav the navigator has not had time to play with to see if it's a good fit.
If you are the English speaking driver, I'd rather you converse with the navigator in Korean and have the navigator use a familiar tool in Korean. Google Maps is available on iOS and Android obviously, and allows pre-loading of offline maps. It keeps them in memory only for 30 days or so, so don't load them too soon or it'll delete them.
Paper maps are your friend
Really. There is no substitute for paper maps. They are large, and present both the entire "big picture" and also the finer details.
However again, they need to be in the navigator's language. Sourcing Korean language maps of the US Grand Canyon ... in the US ... may be a challenge; get them at home.
The "Rescue Me" button
I mention this because this happens at least a couple times a year, usually in the winter. People make wrong turns (often due to sat-nav telling them to), the car has a problem, and they die out there. Every case could have been trivially solved with one piece of tech: The 406 MHz ELT. This uses the military-grade, built-for-purpose distress signal system also used by jetliners and cruise ships. Due to the high cost of the infrastructure (many satellites), there is one world system with all the major powers onboard. A handheld beacon costs about $400 (once, no annual fee) and they can also be rented. It has exactly one job. Break seal, push button, forget it, focus on survival, and 2-12 hours later, help appears. It doesn't do anything else. It works anywhere but the steepest canyons (and obviously not caves), but this time of year you should be staying out of slot canyons anyway. If you have a mind to do anything slightly adventurous, or just if you're bad at navigation, think about getting one of these.
"Continue straight here. Do not get on the freeway."
"At the next opportunity, do a U-turn. We do need the freeway, after all. I wasn't sure, and I called straight because it would be easier to recover."
"OK, good call."
"Get on the freeway northbound. This ramp here, follow the brown truck".