Some colleges do limit direct admission to those majors, but may admit some applicants as undeclared, since some applicants may prioritize attending the school rather than the particular major. But any among the latter who prioritize the major may not want to attend if getting into the major later is highly competitive.
In other cases, there may be admission to the division as undeclared (including first-year-engineering (FYE) programs at places like Purdue, Texas A&M, Minnesota, Virginia Tech, NCSU, Ohio State, Penn State, etc.), but some majors do not have the capacity to admit all interested students, so they have GPA minimums or competitive admission. Note that even Cornell engineering has a similar system, but it is rarely noticed because the GPA minimums to enter the major are in the 2.x range.
Wisconsin engineering overadmits directly to majors and then weeds out with GPA requirements that can be as high as 3.5 technical and 3.0 overall. UIUC also does this with some majors, but it is rarely noticed due to GPA requirements of 2.25 or so. Obviously, a prospective engineering student would be more concerned about meeting the 3.5 at Wisconsin than the 2.25 at UIUC.
As noted by another poster, it is common for nursing programs to have high GPA based or competitive admission to the nursing major after a student takes prerequisites as a pre-nursing student. Business majors at some colleges have similar arrangements.
For the purpose of this thread, let’s say that the parents are fine with whatever major the student chooses, and there is no parental pressure for a particular major, and that the major in question happens to be the student’s first choice.
Note that liberal arts majors like psychology, economics, art, or math may also be subject to admission processes for undeclared students who want to enter them. So the issues that this thread is about can affect students interested in liberal arts majors as well as pre-professional majors.