That's a very good question!

TL;DR: I think for the most part it's because Doctor Who started with TV in its infancy, and it was a very minor show. So the quality is spotty. But it may also signal how common behaviors have shifted over the past 50 years.

---

TV in its infancy: TV had really not been around very long when Doctor Who came along, and shows were feeling their way. A lot of TV was more like a stage play put on by a local amateur theater. with adults playing children. Do you remember Charlie X of Star Trek? Samd problem. Like the primitive sets and costumes, we just accepted the actors playing kids because we'd never seen anything better. I never questioned Susan as a teenager or noticed anything odd about her behavior when I was 11. High school students were older and bigger and wiser than me, after all -- they looked like adults!

It also helped that apart from Dodo (the least popular of the bunch), most of the teenagers on Doctor Who were "unearthly children." Zoe and Adric were apparently meant to be something like 15-year-old (?) geniuses, and Nyssa and Vicki weren't from our time period or culture either. They're Wesleys, not Buffys.

Minor show: In the BBC's full lineup, Doctor Who wasn't that important, despite its cult popularity, so the most experienced scriptwriters were probably working on other shows. It was Verity's first big show. Carole Ann's first big part. I love 'em, but a lot of the companion-actors weren't the most experienced, were they? Trying to act not-your-age may be as hard as trying to put on a convincing British accent if you're American, and vice versa.

Another factor may be who wrote SF scripts. What do you want to bet that white male geeks and nerds spent a lot more time thinking about outer space, aliens and science than they did about what real women or children are like? Zoe rattling off astrophysics is what people imagined kids of the future would be like, in an era when space had caught popular imagination and the future seemed to be bright.

But I wonder if, to some extent, what we're seeing is actually reflective of how children and young adults have changed over the last 50 years. Children used to be expected to act like young adults as quickly as possible. Adolescence underwent a dramatic transformation in western culture in the 50s and 60s, and it took the older generation (those writing the scripts and acting the characters and making the shows) a little while to catch up. Even schooling was different in those days; a lot of the children watching Doctor Who were studying Latin and biology at the age of 10, whereas now... not so much, or not at the same level.

The women acting younger than their age is dicier. How much of that, again, is due to the sexism of the scripts and audience expectations, and how much of that was real women acting that way because it's how culture and upbringing pressured them to be? See Marilyn Monroe: sex symbol who often sounds/acts like an adolescent girl. Women were called "girls" at an age when boys were called "men" The Campion books written during the 30s by Margery Allingham keep jarring me by having men marrying younger women, calling them "kids." Descriptions emphasize the female characters' childlike voices, faces, or behaviors.

Doctor Who gradually eased into having women act more mature, until we got to Sarah Jane (although her maturity was toned down-- look at her Andy Panda outfit). But it came in fits and starts. Writers didn't know how to write Liz Shaw, a Cambridge scientist and professional who really was an adult, and I admit I was lukewarm to her when I was little because she was intimidating. So, after a season, Liz was swapped out for Jo, a younger and more clueless character who would ask the Doctor questions. Leela was a strong character, but not too strong, she was childlike. That appeased sexist audience expectations, or, if you want to be more charitable, it ensured the Doctor was still the leader and still had to Explain Things to his inexperienced companion (and us).


ETA: and I think I kinda slipped off topic and missed the Kiddie Kid trope, sorry. I dunno. It's what adults thought kids liked in kids' shows -- all the Saturday morning cartoons were doing it in the 70s -- and again, we didn't know there was any better way so we accepted it? Just like we accepted one-dimensional villains and other archetypes. :/