It is not known if the Gra agreed with the establishment of an institution "yeshiva" as independent from the local Rav and community. {That is something like a corporation.] For the most part, all you had was the local place where people prayed in the morning and then who ever wanted to just stayed and learned there during the day.

When Rav Chaim of Voloshin asked the Gra about starting such an independent institution as a yeshiva the Gra did not answer at first. Then there are several accounts. Some say that he agreed in the end. Others say he never agreed.

To me this shows a basic ambiguity about the whole issue. Certainly, Torah was never meant to be a means to get a kollel pay check. On the other hand, I had been part of two very great Litvak yeshivot Shar Yashuv and the Mir in NY.   In Shar Yashuv I learned about the great importance of reviewing everything you learn ten times.

So it is hard to know. Maybe the connection between Torah and Money nowadays has just gotten too out of hand.

[I do not know if it matters to others, but perhaps a bit of personal information might be helpful. I had a great time in Shar Yashuv and learned from Naphtali Yeager about the infinite depths of Tosphot. But after that I went to the Mir where the learning was more along the lines of Rav Haim of Brisk. ]