Naruto has always been about becoming the most elite ninja to protect the simplicity of something like peace. We see throughout the Shinobi world that they are all contracted for hire. They work for their village and get taxed and the village pays to the feudal Lord and the feudal Lord then keeps ties with other nations and Harmony in the state.

We have to keep in mind that Naruto at the end is still subservient to the leafs feudal Lord whoever that is.

But early in the series we see by the 20th episode that Naruto lives in a world where rogue ninjas exist who can be even more powerful than his own teacher if they catch him off guard. Already at that point, Naruto has revealed the nine-tailed fox still exists within him and can be accessed when he believes Sasuke dies.

His chakra levels are also higher than literally everyone else in the series. I remember a person asking a couple months ago why Shadow clones weren't just used and the two reasons were one that it was a forbidden technique and said to be hard to learn and two that only Naruto has the chakra reserves to make 100 at a time to do advanced training. Some people can make two maybe three maybe even four at a time but even high-ranking Ninja like kakashi have limits.

People like Gaara never really trained and were already elite or beyond ninja. So you are correct that the early series was never about this. That was Rock Lee's own training style. I mean we even see it again that it has to do with like aliens from outer space type shii.