This^^ is the point.
IF the primary goal is “someplace that will better than this for me”, then only applying to the highly rejective options is not a good strategy.
There are other places that meet full need for international students, but are need-aware- but a student whose profile is strong enough to make them a credible applicant to, say, MIT is a student whose profile is likely to look dazzling to, say, a Union College or University of Rochester, both of whom are need aware but meet need for international students.
On the other hand, if the primary goal is to only move if it’s to a tippy-top name, then the OP’s strategy, whatever the likelihood of success, is just fine.