At its purest, the teen sidekick is a simple derivation of the lead character's core concept. Robin wasn't Batboy or Batty or anything like that, but he was given another flying creature's name, was also an orphan, and shared Batman's abilities and utility belt. The difference was that in making him younger, his creators Bob Kane, Bill Finger and Jerry Robinson gave him a more youthful outlook. He was a more positive version of Batman, a creature of the day, not of the night. And indeed, his presence lightened Batman's adventures right up. Unlike Robin, most teenage sidekicks wear a costume substantially similar to their father/mother figure, and are born of the same question as other derivations: What would the hero be like if he/she were young/the opposite sex/an animal?
Once you have a formula, it's time to introduce twist. The Star-Spangled Kid, for example, was teen with an adult sidekick, Stripesy. Superboy was a teen version of Superman, but not a sidekick, just retroactively introduced adventures of Superman at an earlier age. Wonder Girl was the same until she was repurposed as a separate character in Teen Titans. I would be remiss if I didn't also talk about adult sidekicks who, for some reason, are often from minority groups. Kato is probably the prototype, though Tonto precedes him by a few years, but the idea of giving a lead white hero a minority sidekick was reproduced several times - Wing, Stuff the Chinatown Kid, the Falcon, even Rhodey (the way he's used today). Their status as sidekicks means they are perceived as secondary to the white lead, and through the history of the sidekick archetype, made equivalent to immature teenagers or children. A better name for them would be Partners, but unless they share the billing (which the Falcon did, at one point), it's hard to see them as equals.
But is the adult "partner" the future of sidekickery? Are we too cynical and p.c. to accept teenage sidekicks anymore? Have comics moved away from children's escapism and into a faux-realism where violence is too real for underage characters to be put at risk? These are questions readers and writers are struggling with today. What do you think?