But I would argue that the best scholars of those institutions study the material in more depth and in a livelier environment, considering the context of monastic debate.
Also, academic study of the Buddhist texts is greatly hindered from a practice perspective by the necessarily atheistic template of research at the modern universities. Don't get me wrong, I am grateful for critical academic studies and find them fascinating and informative reading, but I don't think a poor practitioner thinking of enrolling in an expensive university program for "their practice" would find it the best go.
That's unfortunate, isn't it? A scholar with the title of Geshe or Khenpo, and they don't adequately study the ancestral language of their textual tradition(s).
I still think the classical Tibetan and Chinese traditions are very much "living" traditions. For whatever reasons, the Mahayana world is not like the Theravada world where Pali is the scholastic lingua franca. The Tibetans still manage to have a pretty good degree of scholarship and a wide variety of viewpoints on difficult topics within their own language.
Where I do see the gap, though, is in the knowledge of "outside tenants". Jamyang Shaypa's "Great Exposition of Tenants" for example includes some very mistaken interpretations of Indian schools of Sanatana Dharma. Perhaps with Sanskrit scholarship such misunderstandings would have been less rife.