It is not a matter of need. It is a matter of value for the intended purpose. I had a similar vintage truck towing 6000-7000 pounds. It was fine on relatively flat Michigan, but up-hill freeway on-ramps kind of sucked. Enter 6-spd transmissions circa 2007+. THose aren't $10k. The only way to get similar power for those older trucks is 3/4 ton 425+ lb-ft of engine torque. For someone that lives near mountains, you want a lot ore power/gearing than half tons had in 2000-2005.
2003 Tahoe had a base tow rating of 5700 pounds. Some have as high as 7400 pounds. Axle ratio and HD trans cooler are hard to filter on-line searches. Why bother? Availibility? Plenty of 3/4 tons out there. Unloaded ride and fuel economy? OP doesn't care, as he won't use it that way.
Utility of an SUV for a single person and dog - I favored my pickup over my SUV, despite the lower ratings and capabilities.