In the UK it's exactly the opposite. Here's the best case (UCL - a super research intensive university): https://www.ucl.ac.uk/students/fees-and-funding/how-ucl-uses... Most other universities rely far more on teaching. Tuition fees also have the advantage that they are constant and relatively easy to predict while grants last a few years at best (and of course you do have to >do< something with them so they are not pure profit. Broadly, grants are the delicious froth on top of the tuition fee latte.

It’s not always true. I know an undergrad who had a conference paper out in a direction a PI could use in grant writing.