Remember these tow ratings are WITH weight distributing, not dead weight.
I tow a 24' v-nose race car trailer probably 10,000 miles a year with my 6.2L Denali. Total towed weight, certified on a Cat scale fully loaded, is 6,700 lbs with a 900lb tongue weight. I use a Reese DualCam weight distributing platform with 1,000 lb spring bars to get the truck and trailer level. Stability-wise the Denali is fantastic towing the trailer. But from a performance standpoint the truck is barely marginal towing this much weight over long distances especially in the mountains. Until I put a big auxiliary trans cooler on my trans temps would regularly hit 250, and water temps would go way up when towing uphill at 65mph in 3rd gear. Trans cooler brought trans temps down to the 210 range when climbing but still higher than I'd like. And 6.5-7.5 mpg on premium fuel means an expensive fuel stop every 140 miles (2 hours). Oh and I've done a trans service twice- 40k and 80k- to keep the trans alive.
When my rear shocks and pump went (and with all that tongue weight they will blow out) I replaced with Arnott Bilstein air shock and their pump kit. Nice products. But with 900# tongue weight the shocks won't pump up the weight without the spring bars to level it out. OE shocks and pump wouldn't either. Too much tongue weight.
Note- the correct way to hook up a trailer when using weight distributing spring bars is to first shut off the truck so the air compressor does not turn on. Then hook up, level everything with the spring bars to get most of the tongue weight minimized. Then as a last step start the truck and let the airbags air up. This method lets the spring bars do the weight lifting and the air bags just supplement.