GVWR is often less than the sum of GAWRs because GVWR can be assigned to a vehicle for tax and licensing purposes.
For your truck, 10,000 is the max for a DOT Class 2 vehicle, category in which the F-250 is sold, and measured for emissions and CAFE. With the same equipment, it could have a 11,300 GVWR as an F-350, which is DOT Class 2, allowed to go to 14,000 pounds.
Model year matters, as the DOT categories evolve. Class 1 was once limited to 6000 pounds, but moved up as standard size vehicles got heavier over the past 60 years. You'll now find "1/2" tons with GVWR at least as high as 8600 pounds, which was once "3/4 ton" territory.