Ebisu???? Kakashi was smarter than that
Might be a weird title but hear me out.
Alright we all know that Naruto asks Kakashi to train him after the Chuunin Exam prelims for the finals and Kakashi flat out refuses him and goes off to train the prodigy while passing off Naruto too a less than satisfactory teacher.
Defining in that in a lot of fanfiction they use this scene to make Kakashi into a huge prick that cares absolutely nothing about his two other students. And the fact a lot of people use it to show the favoritism Kakashi has for Sasuke over Naruto. Even though it's the only time in the manga we see something like this.
Everyone knows that Kakashi adopted Obito's quote about People being lower than trash for leaving comrades behind. So a thought just popped into my head, what if Kakashi set up the slight training with Ebisu as a precursor to Naruto meeting Jiraiya.
Situation is that Kakashi absolutely knows that Sasuke is going to need intense personal training to even come out alive in a fight against Gaara (also why he taught him Lee's taijutsu considering it's the only thing that they knew could work against the sand, if it ain't broke don't fix it). Considering he is one of Konoha's top ninja, I don't see him not knowing a certain someone is rumored to be in the village, or at least on his way back.
So he calls up the favor he has from Ebisu to help train Naruto (knowing that Jiraiya's training methods weren't with a whole lot of theoretical knowledge). And with a whisper in his ear about how pathetic Naruto's chakra control is and how falling into hot springs will make him learn quicker. Proceed forward and you have Ebisu teaching things Naruto probably didn't learn in the Academy (various reasons for that) and the beginning of water walking. Lo and behold they find someone peeking, and Ebisu being a man of strong moral fiber (denying he is even a closet pervert) confronts him and gets beaten down in full view of Naruto. The Gallant Jiraiya hears the name of his godson and takes him as an apprentice and teaches him skills that he could use in a month (could see Jiraiya knowing about Gaara and how likely he was going to be involved in Oro's plans so he gets Naruto something that would be able to fight against a jinchuuriki using it's demon's form while also improving his chakra control).
I'm taking a lot of things for granted, mostly the fact that Kakashi has pretty much figured that Naruto is Minato's son by now (for who but only the willfully blind couldn't see Naruto for who he is). And the fact that Kakashi knows enough about the going ons about Konoha that he'd know when Jiraiya was in town. But I can see this happening really easily.
The fact that Sakura only sits on her ass for that month is because Kakashi doesn't know what to do with her. He knows she has a great mind and excellent chakra control (precludes her to being a med-nin) but he either isn't connected enough to get her an apprenticeship in the hospital, or he wants his students to have the best. With Naruto it was passing him off to Jiraiya, probably the best person to teach him the way Naruto needed to be taught. With Sasuke it was himself, because he has the sharingan and is probably considered the best ninjutsu user in Konoha at the time bar Hiruzen. Finally with Sakura I guess you could say he was hoping for Tsunade to come back but that's probably stretching too far.
Plausible because we see how much Kakashi objected to the fact that he lost his whole team within the matter of days-a week or two. Which is to say was practically no objections from him. He's smart enough to see that he isn't the best teacher for Naruto or Sakura. His style doesn't match to either of them. He's a quick hitter with one hit kill moves and is more speed based. Sakura is a med-nin thru and thru and it's not something that he could teach because he doesn't have extensive knowledge of it. Finally, Naruto is someone who thrives on unpredictability and never giving up, something that Kakashi can't teach with any proficiency, seeing as he was the "Genius" of his generation.
I think Kakashi came to these realizations after having him do the tree-climbing exercise in Wave or even before that. So instead of teaching them individual things he focused on their teamwork and making them become the best of friends, because you can possibly see how he's lived with the regret that he only considered Obito a friend rather than a nuisance only hours before he died. So he doesn't want his team to feel the same regrets he has.
Now I don't know if this was brought up before (why Kakashi didn't physically train Naruto and Sakura while he personally trained Sasuke), but I've never seen anything about how Kakashi set up the meeting between Naruto and Jiraiya knowing the Jiraiya would take up Naruto's training because of who Naruto is. Guess that'll be all.