University of Washington (Seattle) has a similar system in which some majors are 'capacity constrained' meaning some students would be directly admitted to the program, but the vast majority of them would only enter the major program after being accepted via application while already attending school.

Highly competitive programs included Business and Engineering, but this even spilled over into less popular STEM variants like Math. Their CS program was and is the most competitive of these. At its worst an application round would have ~2000 applications and only ~600 open slots.

During my time there, I met a handful of students that had applied every session for the last few years to no avail. The opportunity cost is enormous. It's both a waste of time and money on the part of the students to spend multiple years wasted taking intermediate courses, retaking major-application required courses and reapplying. That's why the administration is slowly converting over to deciding major on admission, too much visible grievance on the part of students.

That aside, if it's competitive enough, it turns into a second college admissions process. Students retake the core classes required for an application like they would retake the SAT or ACT. Never mind that they passed CS 142 with a 3.4, only a 4.0 will get them in so they waste a quarter perfecting the most basic java programs for content they learned a few months prior. Students also try to engineer around the competition: a common refrain was that the equivalent courses at community college were much easier, but given the same weight in the admissions process so students would go to another college to take an easier course just to have a better shot at their dream major.

The point is that the competition for these colleges will come to a head somewhere. If it's not the college application process then it will be at the school itself. It can be managed, but putting it off till later leads to a greater burden on the losers of this process. They are faced with the choice of changing majors, changing schools or persisting with the hope that maybe the fifth application will be different than the fourth.

Fostering this kind of environment was a mistake on the part of UW. Perhaps it would have been better if they restricted applications to first years and weeded them out completely from the start like they do in your area, but letting the college admissions process do it might be much more efficient on the part of both the schools and the students.