Colleges care intensely about yield, for two reasons. The first is that it reduces uncertainty in the composition of the incoming class. The second is that it's how, internally, undergraduate admissions offices measure their colleges' relative prestige. Harvard doesn't especially care if it shows up as #4 vs. #1 in US News's capricious rankings one year, but if Harvard loses to Yale in cross-admissions, there'll be hell to pay for the Harvard admissions office. Yield numbers are the "bottom line" regarding how good a job the admissions office has done.
Yield optimization plays a huge role in the process. Harvard, for example, aims for an 80% yield rate and generally rejects any applicant for whom it estimates a lower-than-70% chance of attending, regardless of qualifications (my boss at a prior job knew a former Harvard admissions officer). The "yield probability" is based on a number of factors, but mostly number of campus visits and interviews, in addition to the other schools to which the student applied.
Anyone who really wants to attend a selective school has to clear the yield bar by showing a higher-than-baseline likelihood of attending. Harvard doesn't have a 75% yield rate only because of its prestige and the quality of its program-- although those are obviously very important factors-- but also because it's extremely good at selecting people who will attend.