My family drives a mix of Volvo, Range Rover and VW (with an I-Pace on order). Aside from a few infotainment glitches the RRS has been rock solid in its reliability, as has the VW and Volvo aside from a few deer strikes. According to the latest JD UK Power Survey Landrover is ahead of both BMW and Audi. These are some of the most complex and capable road biassed vehicles money can buy, faults happen but with a 4 year US warranty I don't worry and I never own a vehicle outside of warranty. Jaguar is above average in its' reliability.
Pre-Tata Landrover vehicles are something I would never buy, but the latest generation are good solid vehicles.
The old ones are where Landrover gets that bad reputation.
Should I go for a US SUV instead? Cadiilac Escalade is about as crude as they come, Ford Explorer is cheap and nasty etc. If Landrover is so awful then whey are they having record sales? 2018 RRS is selling above MSRP with long wait times. My second choice for an SUV would be a Volvo.
http://www.jdpower.com/press-releases/2017-uk-vehicle-dependability-study