How does the statement of purpose of students help professors to write letters of recommendation for graduate school application in U.S.?

Usually, professors need to see students' statement of purpose before they write letters of recommendation for them. However,

(1) The most important part of LoRs is the comparison of the applicant with their classmates/peer, which is normally not shown in the statement of purpose.

(2) Professors often talk about students' strengths in LoRs, but they are not supposed to use the strengths mentioned(or boasted of) in the students' statement of purpose when the strengths are unknown to professors before they see the statement of purpose.

(3) Professors may want to know students' experiences, interests and plans for future. But such things are already mentioned in students' statement of purpose and they don't have to repeat them again in the letters of recommendation(professors are not supposed to know students experiences, interests and plans for future better than students themselves, right?).

So my question is, given (1), (2) and (3), why do professors need to look at students' statement of purpose at all when they write LoRs for them? How does the statement of purpose help professors to write letters of recommendation?