Open book exams
A particular reason for time limits is the open book exam. Such an exam without any time limits would allow the student to simply study all the relevant topics on the spot, and be useless for evaluation; however, an open book exam with an appropriate time limit will separate students based on their knowledge and obtained skill, while allowing the benefits of open-book exams for subjects where people aren't expected to memorize everything but use reference material as needed, and in those subject areasdisciplines where you should techteach students a habit to always doublecheck ifand verify in case of doubt, instead of guessing, e.g. medicine.
In essence, the time limit is a tool to check if you need to look up 5% of issues or 95%.