Since I moved to the area seasonally by myself, most of my visits are solo. This doesn't bother me one bit as I am an only child and have lived by myself since college (by choice!), so it feels natural and normal to me! As others have said, it allows you to enjoy the parks at your own pace, and do whatever you want to when you want to. It also allows you to take in all the little details, background music loops, and really immerse yourself in the Magic.
Having said that, when my parents or friends come to visit me, I enjoy sharing the experience with others as well. But I would never want to give up the frequent solo visits completely!
Since I live alone and am an only child and an introvert, I never get "lonely" spending time alone, whether at the parks or anywhere else. (If anything, being constantly around other people 24/7 with no time alone would drain and exhaust me!) I am very independent and have a strong sense of self. I am also deeply in touch with my "inner child" so when I visit the parks I feel like a little kid again, which is a great feeling!
PS. EDIT - This thread reminds me of my earliest solo visits. My parents took me often, but I remember joining a youth group before I started driving solely because they took a trip to WDW every year, and I could never get enough of WDW! I wouldn't mind touring the parks with ONE other person from the group, but as soon as it became a group of more than two, all the other kids wanted to do was walk around in circles all day and be "social". I didn't pay money and look forward to a Disney trip all year to do boring teen stuff, so I would always find an excuse to get seperated and go off alone. Many days I would deliberately start out alone. Back on the bus, when comparing notes with the others, they were amazed that I was able to experience every attraction in the park, and I was amazed that their little groups missed more attractions than they actually experienced. In FULL open-to-close days! Which told me that my instinctive desire to tour solo was the correct choice, as I actually have a passion for the parks and their attractions - much more than the other kids on the trip did. And they considered many of my favorites (such as the Fantasyland attractions and CBJ) to be "kiddie" and beneath their "sophisticated" teen taste! But I was never a teenager, even when I was a teenager!