It was too good, and too cheap.
And everyone trains on T-38’s so they are already familiar with the basic aircraft. But, that would be too logical.
IIRC, an article in the Atlantic around that time pointed out how the Northrop/Grumman(?)F20 lost the battle. Essentially, the reasons you cite.
Why can’t they just use the Warthog as a trainer and an antijihadi ground support - it’s tough and already well established......
Not a fighter, no doubt.
Or bring back the venerable Indian Gnat!