Two things can be true at once. In this case, it's true that people wanted to expand access to education. It's also true that, rather than just subsidizing education properly, this was seen as a more market-oriented approach.

I also don't think it's true that "giving students loans is cheaper than paying tuition directly". Governments are in a unique position to capture broad societal gains through taxation. So I think the cheaper option is just to fund education, especially the sorts we think increase economic productivity, and then tax the resulting income.