We interpret Tech's mission very differently. The GTRI does exactly what you say. But the university within the Institute has a mission to create well rounded, well educated, "total people" who contribute to the betterment of society; through growing, applying, and spreading knowledge. That's why we have athletics, electives, and required courses in humanities. Teaching the next generation of innovators and leaders is essential to that mission. If the mission was as you say, Tech would need to be nothing but the GTRI and a vocational school.
Mission
"Technological change is fundamental to the advancement of the human condition. The Georgia Tech community - students, staff, faculty, and alumni - will realize our motto of "Progress and Service" through effectiveness and innovation in
teaching and learning, our research advances, and entrepreneurship in all sectors of society. We will be leaders in
improving the human condition in Georgia, the United States, and around the globe."
https://www.irp.gatech.edu/gt-visionmission-statements