For generations, students and researchers from around the world have flocked to Boston, drawn not just to a college or university but to a region where high-minded intellectual life was part of its brand. The Boston area has thrived from their presence, its many schools and top-ranked research hospitals keeping its economy strong and its living standard largely unmatched in the United States.

“It’s the densest concentration of academic talent in the world,” said Lawrence S. Bacow, who…