In the early years of Spider-Man, the series was renowned for presenting a teen-age hero who lived a realistic life in a real place with real problems. (Before Spidey, heroes lived in places like Gotham City or Metropolis and their problems consisted of such things as thwarting their girlfriend's efforts to discover their secret identities or dealing with being shown up by a dog in a version of their costume. Even the Fantastic Four started their adventures off in "Central City".) But all evidence points to one other intended innovation from which Stan Lee and others ultimately backed away. Spidey, in his first few years, was aging at a real-time rate.
Take a look at those early issues. Peter Parker is a High School student in Amazing Fantasy #15, August 1962. Let's say he is 15 years old. Three years later, in Amazing Spider-Man #28 (September 1965), he is 18 and graduating from High School. Three months after that in ASM #31 (December 1965), after his summer vacation has ended, he enters Empire State University.
There are other little evidences of the passage of real time. In ASM #7, the Vulture is portrayed as having spent a number of months in prison, after his defeat in ASM #2. On the splash page of ASM #17, Pete thinks, "It's been months since I had that battle with the Green Goblin", a battle that took place in ASM #14. In ASM #23, Pete finds a letter from Ned Leeds, "the reporter who used to date Betty a few months ago". Ned first appeared in ASM #18. Also in #23, Frederick Foswell has served his time and is out of jail. Surely, as the leader of the New York mobs, Foswell had to serve at least a year. He was arrested in ASM #10.
Somewhere along the way, this all ends. It may be the sudden rash of multi-part stories (in which a few days are displayed in many issues) or the realization that Spidey was going to be around for the long haul that caused the change but soon the years mattered little to the web-slinger. But what would the series be like if Spidey had continued to age normally?
By this time, Peter Parker would be about 50 years old. Certainly at this point, he and Mary Jane would have one or two children. (If they started young, they may even be grandparents!) Would Pete still go out and fight crime? Of course! (If he didn't, the series would be over.) But he wouldn't necessarily be fighting the same old foes. There would be a new generation of bad guys. Older villains like the Vulture and Doc Ock would probably have expired by now of natural causes. Aunt May would never have made it to 1995. J. Jonah Jameson and Joe Robertson would be long retired.
Clearly, Pete's way of not aging is much to be preferred. I think I'd like to live that way myself. There are only two drawbacks that I can see. You would have to spend over 30 years in college and, in order to qualify, you would have to be a fictional character.