Alright, we don't even know if Kazekage is nominated like the Hokage. It could, after all, even be birthright.
Second, Gaara controls sand. In the Hidden SAND Village thats an obvious advantage....
Also, he inherits something like a god to them.

After the little war, both sides had a lack of shinobi. That does not mean that new shinobis got promoted any faster! Bad shinobi with high ranks are still bad shinobis who will fail the mission. But it made everyone take overtimes. More missions to fulfill in less time. Therefor, more experience in the same amount of time, compared to before.

Do you think Kakashi would have developed a new jutsu (the 2nd in his life. The first one during a war), if he continued to lazily hang around in Konoha as he did before? Also, he appears right now better worked out (stamina wise etc) than ever before.

Naruto wouldn't have become chuunin or jounin if he stayed in the village. He needed the 'isolation training', so that he had noone to pull off pranksters and focus on his training. Hanging around with just one person, who (a) teaches him and (b) acknowledges him, gave him the needed carefreeness to train, develop and evolve.
Now, that he has overcome the social pressure and is more self-confident, he can finally start to seriously interact with other shinobis.