I for one think Kakashi would be stronger without the Sharingan. Although, as a consequence, his overall potential may be lowered. Let me see if I can clarify this.
Kakashi was already a talented ninja when he was 13, without the Sharingan. He made Jounin, although for all intents and purposes I'd say he was probably only about as strong as Sasuke and Naruto were when they were 13 (I still believe that war lets people advance through the ranks a lot faster than normal). That said, when he first gained the Sharingan, he was by no means at his peak in terms of skill or chakra capacity, so it was probably an enormous ordeal trying to get some balance between using the Sharingan and lasting in battle more than 10 seconds.
So he likely lost a good deal of time that he could have spent improving his skills, trying to master how to use the Sharingan, given his unique situation. Also, as he got older, his chakra capacity, most likely, would have naturally increased, allowing him to actively use his Sharingan more often, and so he did; thus he earned the nick-name Copy Ninja. Basically, he sat back and let his already Jounin level skills and the Sharingan do all the work, rather than push his normal skills higher and utilize the Sharingan as just another part of his arsenal. Basically, without the Sharingan, he would've needed to keep improving in order to really stay competetive and not die.
Without the Sharingan, he would've had to spend time pushing himself to his limits in order to see that massive boost that he immediately got with the Sharingan. Also, he would have to be more skilled to offset the loss of his left eye. In my opinion, he would've been phsyically in much better condition, and his chakra capacity would've been much better because he didn't have the Sharingan using it all up; his jutsu list would've been smaller, but he could've used high level moves more often without fearing of collapsing mid-battle.
Don't forget that Kakashi is also said to have a very good sense of smell, and he has his nin-dogs. Someone who is said to be pretty damned smart could've used both of those aspects to forge a specific style for themselves, much like how Jiraiya specializes in Toad Magic type jutsu. He also had his father's tanto, which I believe he had fixed after being broken; using his father's techniques, his nin-dogs, good sense of smell, (effectively) higher chakra capacity, and (supposedly) very high intellect, he could've been a terror in battle. Note that he also mentions specifically that he was much weaker than he was in his ANBU days, most likely because that was still a period when he couldn't rely on his Sharingan to handle the bulk of his battle for him, since he still had only just gotten it and needed time to adjust.
I think he would be a good deal stronger, initially, but I think that without the Sharingan, his overall potential would be lower though, since the Sharingan is a pretty massive power up, for all its drawbacks. I guess a fair comparison would be to someone like Hiei from Yu Yu Hakusho and his Jagan.
Hiei was an A-class fire demon, but when he got the Jagan it dropped him all the way down to a D-class demon. However, once he got used to it and was able to learn how to actually use it, he kept jumping back up in power, until he was able to fight evenly with S-class demons. So basically, he would be an A-class demon without the Jagan, but an S with it; however, he needed a long time to actually reach the S-class and overcome the Jagan's drawbacks, before he could reach that higher plateau.
Kakashi is no different; he started out as a fairly tough guy, but then he got the Sharingan and it left him in Limbo in terms of fighting, since it was such a huge drain on his chakra. However, in time, as he mastered it and built up his chakra capacity and after training through the timeskip, he managed to combine it with different jutsu and his newly re-developed skills to be able to fight more evenly with guys like Akatsuki; he even managed to pick up the Mangekyou, despite its high price. I also think he still hasn't reached his pinnacle yet; he's still young, and despite his experience, he still has plenty of room to grow.
I know that was sort of off-topic, but I only brought it up to tie in with what I have to offer about your idea.
I think that if Kakashi was without the Sharingan because of this missions, I could see him being a more capable, yet callous leader for Team 7. I don't think he'd favor anyone though, and I think he would be extremely thorough in teaching them/breaking their weaknesses.
The real problem that I see with this is that Team 7 would hate him and wouldn't want to work for him. Hell, he probably wouldn't even get a genin team in this scenario, as he'd probably be hardcore into sticking with ANBU, considering his original beliefs had been so strongly re-affirmed after that mission. And if that wasn't a problem, the next one would be: Kakashi would likely be asked to take over as Hokage when Sandaime dies, considering he would probably fall into that S-class ninja domain, and unlike Tsunade, he's loyal to Konoha and not rusty at all. He also is strictly business, unlike Tsunade or Jiraiya who are drunks and not at all serious.
I think for the fic to work, you'd either have to follow Kakashi by himself, or Team 7 with a new Sensei and have Kakashi fill in as Hokage afterward, and have that be something that effects Team 7, when they have a no-nonsense Hokage who isn't afraid to berate them for failure or idiocy, compared to the gentle Sandaime. The third and probably last option is to have Naruto be apprenticed to Kakashi as a sort of way to curb Naruto's bad behavior/problems and turn him into a capable young man. It would probably work better if you started when he was 9 or so and let Kakashi take charge of Naruto before anything gets too far and force Naruto to take his career seriously. You could have Naruto improve drastically, graduate when he's 10, to keep in line with the 3 failures thing and have him follow Kakashi around and let them work as a team, until Sasuke and Sakura are assigned to them. Naruto and Kakashi are specifically assigned to watchover and help train Sasuke, because Kakashi's got that eye of his and Naruto's proven himself very capable and possibly a good influence for Sasuke, since he turned himself around.
I think those are the major issues, but alternatively, I think all three of those scenarios sound like awesome plots to me. :yay:
