The answer to your question can be found in our experience with Russians a few years ago. When they first came to America, we gave them scholarships and more. We invited them into our homes to join us for Shabbos seudos. We helped them find jobs and tutored their kids for free. However, many eventually pulled their kids out of our school and sent them to public schools anyway.
Getting something for free does not always make people want it. And if you want something, the fact that it costs money doesn’t have to stop you from going and getting it. There are countless stories of people who were moiser nefesh to get things they needed for their spirituality. The bottom line is, if you are not willing to be moiser nefesh, you’re not going to value it enough to be worth the scholarship. Why give a scholarship to someone who will decide tomorrow to go to a ‘different’ free school, which maybe has a better science program?
Maybe your friend would have stayed in Bais Yaacov if it had been free. But if she wasn’t committed to Yiddishkeit, she would have just been a bad influence on you and your classmates. I don’t think we should give scholarships out unless the ONLY problem is the money.