Because what kid hasn't been there? Kids love books they can connect to, just like the rest of us, which is why our reading styles change as we get older. Give a kid a hero who is the same age as him, with the same issues, which remain the same no matter what time period you're talking about, and BAM, kids relate, instant classic.
I know why I loved those books. Because I had a little sister and a little brother, and sometimes I wondered a) WHY my parents ever had any more children, and b) if I was the only normal, sane person in my family. Some days, I would swear on a stack of Bibles that I'm adopted. Just like Peter. Add in the other troubles Judy Blume puts in- moving, making friends, troubles with friends, and school, and ou have the life of any American kid, whether they grew up in the 60s, the 80s, or the 2000s.