Do they? Model X weighs 5600lbs, here - https://www.caranddriver.com/tesla/model-x - and that's bigger than any of the other, more popular, Teslas other than the Cybertruck.
Tesla 3 - up to 4065.
Tesla S - up to 4941.
Tesla X - up to 5531.
Tesla Y - up to 4416.
Chevy Bolt - 3563.
Leaf - up to 3853.
Mach-E - up to 4920.
ID.4 - up to 4848.
E-Tron - up to 5754.
BMW iX - up to 5659.
Taycan - up to 5121
Kona EV - up to 3715.
I like how you just excluded all the comparable EVs. Here they are for completeness, most coming close to or topping out the standard 7k where they will post "No Trucks" signs.
Ford Lightning - 6,893
Hummer EV - 9,063
Rivian R1T - 7,148
Lordstown Endurance - 6,450
Chevrolet Silverado EV - 8,532
RAM 1500 REV - est. 7,500
Alpha Wolf - 7,088
"No truck" signs are for semi trucks, not pickup trucks. These semis (just the truck, no trailer) weigh 2-3x more than an average pickup truck/Cybertruck and 3-5x more than an average EV.