Users want fast access to their mail. They do not want to be delayed by the downloading of N megabytes of unwanted data (like a load of viruses). This is particularly so for those who are still on dial-up access. Those who are bandwidth-billed also do not want their expensive bandwidth wasted. They do not want other people to be able to mailbomb them or DDoS them with mail.
These goals point to a protocol in which the recipient can be very selective about the data transfer process.
I regularly use such a feature with POP, on first try only downloading 10KB or less of a mail is indeed a great way to eliminate a lot of spam and virus bytes and very few interesting bytes. For some time I only did that when on a trip (dialup), but now I'm doing it all the time.