Earlier quoted context omitted.
If if I was trying to solve this problem and actually cared about the students I would do some capacity based pricing. Almost always free, as you approach parking capacity price increases. You could probably also set up a system to text people who have been there more than X hours that they will start to be charged due to high capacity.
The problem is that people need to know in advance to change their behavior: tell them that today will cost $20 and people will take the campus shuttle, bike, or walk. Tell them that you’re charging more after they got there just makes it stressful and won’t change behavior unless it happens often enough to be highly predictable - just like many people drive hoping traffic won’t be bad today because they’re prone to…
If the goal is to make sure there's always a spot available while having the lowest possible price to guarantee that then I think variable pricing based on capacity is better.