I would disagree with you. It is so much more than just a trainer.
Designed in the 1950s, it has done a fantastic job for 50 years in transitioning pilots to supersonic fighters, and a myriad of high-performance heavies and bombers. NASA astronaut trainers, USAF and Navy TPS usage, test squadron aircraft for chasing cruise missiles on low levels. And most recently, a jet used to save hundreds of thousands of dollars in its F-22 adversary support role. Versatile... and impressive. Did you know it briefly held the time to climb record in 1963? And be thankful: had the T-38 not been selected, it would have been an F-100 variant. I'd bet we wouldn't be flying those anymore.
When it came to getting out of Del Rio, Randolph, or Beale on the weekend, the "two-engine, twin-turbine, JP-8 slurpin', dual afterburnin', supersonic bar hopping machine" was the perfect steed. I met a lot of people as a result of the T-38. Even flew six sorties with Steve Ritchie.
I got 5 rides in the T-38 in college; solo'd it in 1985; flew it all over the U.S. in some very challenging conditions, and on gorgeous VFR legs through the Sierra and the Rockies; flew my fini flight on 24 Sept 2014. Some trips were solo, some were with my favorite people. Loved it every time I got in it. And I am a substantially better pilot today because of all the sorties I flew in that jet.
I've got over 100 types of aircraft in my logbook, including 8 sorties in the Viper (one from the front seat), a smattering in the Eagle, two in the T-45, three in the A-4,... F-18B, F-18F... and plenty more. From my perspective, looking at those other 100 types I've gotten stick time in, the T-38 is pretty impressive.
F16 capabilities? Nope. But just because you're married to a Brazilian supermodel doesn't mean every other woman is a let down.
Beauty is in the eye of the beholder.