Personally, I think an exit exam for school (an exam a student needs to graduate from secondary school) is not necessarily the best way to determine if a student has been prepared by their school. That aside, some of sort of assessment of what a student has learned from their school, whatever form that would take, should satisfy an important criterion; that the student is somewhat prepared for the challenges that life will throw at them.
A typical high school exit exam is testing a student’s preparation for one component of life, specifically college academics. It seems obvious to me that this narrow definition of "preparation" doesn’t actually prepare students for the challenges of life. A student could quite easily pass the NY Regent’s exam in mathematics, any of the IB mathematics exams, their SAT, and any number of other standardized exams, and not know a lick about how to apply the mathematics they are learning in school to solving problems they will encounter in life.
While this shouldn’t be the only goal for mathematics education from K to 12, it seems to me to be a minimal goal, and one which at which we are failing quite dramaticly. Some evidence of this failure is seen by our mostly innumerate public who; lack basic literacy of graphs & statistics, are largely mathphobic, do not understand probability (casinos are good evidence for this), and generally only use relatively simplistic mathematics in their day to day life for problem solving.
There is nothing inherently wrong with teaching how to do a calculation for it’s own sake, or for sharing some of the beauty and power of mathematics, but it should be framed by the notion that our education of mathematics is intended for a greater purpose. If we only focus on the 4 years people spend in college, we do a disservice to the decades of life they have after college.