Every school wants to fill its class with people who are enthusiastic about the school. Schools are concerned with "yield" which is the ratio of offers to matriculants. Some schools will make 400 offers to fill 100 seats -- this happens at highly ranked schools (when every successful applicant has 3 or 4 offers some of those schools are going to be disappointed).
So, anything that indicates a strong interest or commitment to the school is a positive. If three generations of Sniggerhufs graduated from the school ahead of you and you learned the school fight song before you learned your nursey rhymes, then perhaps you have a strong desire to attend. The school hopes so.
The darker side is that if your daddy, grandpappy and great-uncle Louie have been donating $1,000 year for the past 30 years (and $10,000 in reunion years), and you don't even get an interview, those generous donors may be upset. If no one in the admissions office knew your relation to the very generous Drs. Sniggerhuf, the alumni office is going to be in a tizzy about the unintentional insult to its donors. So, adcom offices ask to avoid an embarassing faux pas.
When all is said & done, applicants get a numberical score. Let's say its a scale from 0-100. (No extra points for legacies.) Let's say that the school has 300 letters to send with the hope of filling 100 seats. Starting at the top of the list and working down, the first 295 letters go the applicants who have a "score" (based on application & interview) of 92-100. Now there are 5 letters left and 60 applicants with a score of 91. Which 5 applicants get the letters? All else being equal, it is likely that legacy or URM or some other special circumstance is going to tip the balance.