Well, two things.
First, it's not exactly a kids show. It started as such, and is often appreciated by kids, but since the relaunch, I don't see it as truly a kids show in the sense of "For kids ages 5 to 11." It's scary, and it's got plenty of sexytimes stuff in it, and emotional drama. I'd say that the emotional maturity of the show is targeted at teens, actually. Like, if I were going to say what the "sweet spot" is for Doctor Who's demographic, it'd be teenagers and pre-teens. Since the David Tennant seasons, I'd especially say teenage/pre-teen girls. But there's also a lot of adults who enjoy it -- and who are buying the merchandise. That's the other thing. Doctor Who has become a MASSIVE merchandising force, and one that targets a very broad demographic. Based on that, I'd say that while it was originally a kids show, it has morphed into something else, at least in the last decade since the relaunch.
Second, as for the whole "It was a rewrite" thing, earlier in the year, there was a whole bunch of news about how Jenna Coleman was leaving after this season, and that this would be Clara's last year. Then, I think after the series finale, it became more of a question as to whether she was or wasn't leaving, and they left it as a "mystery."
Some fans LOVE her. I tend to think this is the teen/pre-teen girl (or folks with those sensibilities) market, because Clara acts both as their "agent" as a kind of "wish fulfillment" for them. Which is fine. I mean, God knows there's plenty of "wish fulfillment/agent" material for the same age bracket for boys.
Other fans HATE her. I tend to think that this group is a mix of the guys who want the focus back on the Doctor, and some women who took issue with Clara's "Manic Pixie Dream Girl" nature in Matt Smith's last season. Which, in my opinion, is a fair criticism. Clara didn't have much personality last year, other than to be this intriguing "impossible girl" that was destined to save the Doctor and blah blah blah.
Personally, I really liked Clara's development this past season. They made her into more of a fleshed out character. They gave her a life, they gave her flaws (big ones, in my opinion), and they seemed to be using her to illustrate why, as much fun as it may seem to travel with the Doctor, there are real dangers. Not just to life and limb (although there are those, certainly), but to your happiness. Travel with the Doctor comes at a price. Other companions have paid it in a sense, and then still found meaning in their lives, but near as I can tell, only Clara has TRULY lost aspects of her life because she chose to travel with the Doctor (indeed, one could argue, because of her addiction to the Doctor). I found that really interesting, and not exactly something that had been explored. We'd seen things like "Oh, you might die" or "Oh you might feel sad after," but we hadn't seen as much about how traveling with the Doctor could actually ruin the rest of your life if you aren't careful. With the season finale, it seemed like they'd put a period on that statement. Right up until Santa showed up, that is. The Christmas Special, however, did a decent job of continuing that and giving Clara a happier ending if not necessarily a happy ending. Right up until the THIRD dream-within-a-dream thing happened and the Doctor woke her up AGAIN, and they jaunted off together again in the TARDIS.
I think it's the emotional whipsawing, coupled with the news about Jenna leaving -- wait, no! -- staying, that made me think the ending was tacked on. Also there's been news that they basically had to rewrite the scripts for Season 9. Whether that means that Clara AND Shona will travel with the Doctor, I don't know. That could be an interesting dynamic to explore, too -- the sibling rivalry thing -- but we'll see. They might just as easily ignore Shona until next year.
