You do not really see in the Gra the idea of making yeshivot. And if he agreed with Rav Chaim of Voloshin about this is not clear. [Rav Chaim had come to ask him about this and there are a few versions of what the answer was. Some say he never answered.]  

So while this issue is unclear, there are at least some points which are clear. Torah is not supposed to be a means of making money. While on one hand learning Torah is the greatest of all mitzvot, still the general approach of yeshivot going around asking for money does not really mean that this is a good thing.

The religious seem intent on using Torah in one way or the other to get profit. In fact. I encountered a sort of odd attitude in which people in kollel would present themselves as "astronauts" [super achievers] which therefore deserved to be supported by all us plebeians. So it seems impossible to say that people in kollel are not doing it for money. Just the opposite--that seems to be their entire intension.

So what is the best thing is to learn Torah, but not to make a business out of it.

If you are learning Torah [which you should] then you should trust in God to support you. And if that trust is not fulfilled and you find yourself in need then you should find a job, but not go around asking people for money to support you. That is not trust in God. That is trust in flesh and blood. That is trust of the Dark Side