Drove mine from NY to FL, 2 times. No issue it was pretty much like driving a car down and back. As long as your suspension is pretty firm you should be good.
Just keep your expectations realistic…the JL isn’t a BMW X5. Blows around in the wind, is noisy, a bit bumpy, and steers like the solid axle vehicle it is. I drive mine to Colorado a couple times a year (1,100 mile R/T). Fun in the trails, not so much on the long drive. Certainly tolerable but nothing like a nice SUV. As would be expected when driving an aerodynamic brick, gas mileage is especially poor if fighting a strong wind or driving at high speeds.
My 2dr JLR didn't wander at all and seemed rock-solid on my first long freeway road trip when it was new, stock 33" tires. 2000 mile trip mostly freeway. I drove a lifted TJ on 33s for 22 years so I wondered if I'm just too used to the wander effect, but my co-driver on that trip said she didn't notice any wander when she was at the wheel. Later on I installed the Mopar lift lower control arms in preparation for 35s, and it really slowed down and stabilized the steering on 33s. Slower than I liked. When I got the 35s on though, it was perfect. Somewhat slower steering than stock LCAs with stock 33s, and feels perfect now.
Like others mentioned, it's not a road car and you shouldn't expect it to feel like one or steer like one, but my 2dr JLR is so different from my old TJ for road trip comfort. Loved that TJ but while driving the freeway a few hours to trailheads, in the TJ you never forgot you're in a rumbly tin-can. The JLR doesn't have any of that effect--it's almost too quiet and calm and smooth for a Jeep. Not complaining because it's still clear you're driving a Jeep, but it surprises me how plausibly it performs the role for roadtrips. Part of the surprise for me was that the 2.0T manages freeway speeds with ease, and then excels when the freeway is at altitude here in the mountains.