Admission rate alone may not give the full picture. It is certainly possible that the UIUC applicant pool for CS may be stronger than the overall UIUC applicant pool, so the difference between 4% of a stronger applicant pool versus 60% for the overall applicant pool is greater than just the admission rate difference suggests. Also, applicants to popular majors like CS at UIUC may get admitted to second choice majors or DGS (general undeclared) instead, adding to the overall admission rate.
A different kind of example is San Jose State University, which uses a non-holistic admission process that basically ranks frosh applicants by HS GPA (recalculated with limited weighting, maximum about 4.3-4.4), but with a few categories of bonus points (e.g. local area students get the equivalent of +0.25). For CS, the fall 2021 admission threshold was equivalent to a 4.25 HS GPA, even though many other majors had admission thresholds equivalent to a 2.50 HS GPA. Freshmen Impaction Results | Admissions