For example, if I apply as a Mechanical Engineer to Harvard, Stanford, and MIT, and assuming my applications to all three were equivalent in quality, would I have a better shot at getting into Harvard simply because Stanford and MIT are top-tier engineering schools?
many schools don’t consider potential majors (like Harard). Accept rates are determined by #s of app/# of openings. You’re asking a non-comparable question. This hypothetical application would NOT have the same admit likelihood at each schools b/c each acts completely independently, with its own criteria.
But since you brought up Harvard, Stanford and MIT — what material difference would it mean to any individual applicant if the admit rate is 5.4% vs 5.6%. Really?
If you’re a viable applicant and enjoy all three, you should apply to all three. The varying admit rates by each for Mech Eng should be irrelevant to you since they’re each so minuscule.