According to the TireRack site - which you like to reference - the Michelin Premier LTX is described as "Michelin's Crossover/SUV Touring All-Season light truck tire developed for the drivers of crossovers, sport utility vehicles, light-duty vans and pickup trucks."Soft sidewalls are indicative of a "Touring" All Season tire. Designed for comfort. The Michelin Premier LTX is a touring tire with a softer sidewall. Then yes, if you want a tire more for a light truck, then you will have a stiffer sidewall, like the Michelin Defender All Season (not a touring tire) which is not available in the OPs size. If I were looking for a stiffer sidewall for a 20 inch rim, I'd look in the High Performance category. Like the Goodyear Eagle or the Sumitomo HTR AS P02. These are not exactly the best for snow or ice condition, but will certainly satisfy a person's desire for a more spirited drive at highway speeds.
What Michelin tire are you recomending?
Whereas, the Sumitomo HTR A/S P02 - which you like to recommend - is described as "High Performance All-Season radials developed to meet the year-round driving needs of sports car, sporty coupe and performance sedan drivers."
Do you see any mention of that tire being suitable for SUVs?
If you want a "performance" type tire for an SUV/crossover, then look to the Pirelli Scorpion Zero All-Season or the Toyo Proxes ST III.
SCORPION™ ZERO ALL SEASON 245/50R20 | Pirelli