In my opinion, if you have multiple children, you need to set a budget for your first child that you can also afford to pay for ALL of your children. Then insist that they stick with the budget.
You should try to minimize or avoid debt if this is reasonably possible. It is not always possible to avoid debt. Both of our daughters discovered after graduating from university that having avoided debt was very helpful in terms of what they could do next. Many first jobs after university do not pay very well, but can provide valuable experience.
Many, probably most students are restricted by their budget in terms of which universities they can afford to attend. In our case our budget did restrict which universities our daughters could attend, but they were able to find appropriate universities that were academically strong, were a good fit, and that fit the budget without debt.