Interesting topic.
I do agree that Kovus transformation goes by rather quickly, but for me, that just confirms that he`s not the cold blooded killer that Scar was, he doesn`t seem to have that darkness in him. The way I look at it, Kovu has a much gentler nature, he`s a softie at heart. There is for example a deleted scene from SP where Cub Kovu is seen chasing a bug, he catches it only to release it. Zira comes over to him and crushes the bug, telling Kovu there is no room for weakness. Although this scene was not included in the final movie, I think it shows that (as a cub, in any case) Kovu showed signs of a gentle, kind nature.
Now, he was trained and brainwashed by Zira throughout his life, and of course that would take a very long time for him to get over, way longer than what is shown in the movie.. of course, Disney movies usually don`t strive for realism, so you have to take some things with a pinch of salt.
The way I see it, the writers intended for Kovus transformation/change of heart to occur due to him falling in love with Kiara, but I also think he was never that cold or hard to begin with..
Anyway, regarding Kovu and Kiara as rulers...
It`s true that Simba never recieved any proper training. He`d barely learned that he would become king before Mufasa died. We see in SP that he seems to be following Mufasas laws, and I can`t imagine Mufasa had time to teach him much before his tragic passing. As for Nala, she grew up as just a normal cub in the pride, but she is sensible and wise in my opinion, and I think she makes a great support for Simba and a good queen. I don`t think Sarabi recieved any training either (if we assume that Mufasa was the crownprince) and yet she seemed to perform her tasks well.
It`s only mentioned once in the movie that Kiara will one day become queen, and as a cub she is very reluctant to embrace her role in the pride, unwilling to take on the massive responsibility that comes with her regal position. This issue is never brought up again when Kiara is older (which annoys me to no end) so we don`t know how she feels about becoming queen now that she`s a young adult.
Would she make a good queen? Hard to say. She`s still quite young by the end of SP, and like it has been mentioned, it`s not like her father recieved much training, so one can wonder how much wisdom he can pass on to his daughter. I think that when Kiara becomes older and more excperienced, she`d be better suited to deal with being queen. If she were to become queen when SP ended, I don`t think she would have done a good job, as she`s too young and still in much need of her parents support.
As for Kovu, I don`t see him as a leader.. And considering his background, he is bound to carry some baggage, regardless of how he might have changed when getting to know Kiara and learning to enjoy life. I`m not sure how well both Kovu and Kiara can deal with pressure... then again, Simba and Nala seem to be doing fine, and it`s not like either of them were very prepared to rule the Pride Lands when they were young.
So, to sum up.. I don`t think Kovu would make a good king (though I suspect most of the desicion making and law passing would be done by Kiara, as she is the royal heir)
And Kiara as queen? Give her a few more years to gain maturity and wisdom, and I think she`d do OK, but not as well as Nala or Sarabi before her.