Purdue’s transition to major stats are similar to TAMU’s. I believe we were told 94% of students get their 1st or 2nd choice major.
Schools that don’t have a competitive transition to major program still have a lot of self attrition. My dh is a Cornell engineer. Many many of his cohorts transferred to other majors after bombing first year calc, physics, or chem classes. Engineering is tough at every ABET accredited program, many students are ill prepared for the rigor, and self select into different majors.