It was a fad of the era which followed on from the excitement of all-jet training ( which itself declined in the 1970s ). The British RAF looked at the T-38 as

It was a fad of the era which followed on from the excitement of all-jet training ( which itself declined in the 1970s ). The British RAF looked at the T-38 as inspiration but the subsequent Jaguar turned out as an attack aircraft. The Japanese then looked at the original supersonic training concept of the Jaguar and cloned it as the T-2, larger than the T-38 but likewise still in service. The few other forces who ended-up using T-38s did so as a result of FMS credits rather than actual need or validity, since the US had nothing to offer comparable to the subsonic Hawk and Alpha Jet.