Agree with Obito and Rin relationship being underestimated, though I think Obito and Kakashi relationship isn't an understatement. In our lives sometimes we don't get to choose who we have as team mates, or when we do projects in school, in a way our teams assignment are a part of being fated together. The very best we can do is actually for the team as a whole to make the best of it. In the case of the ninja story this is even more so, as the team is a matter of work-mission and life and death.

The occupation that the ninja role took was not one like a regular civilian it is literally the path of a soldier. I think being on the same team meant a lot more than just a project it means being able to be there for each other when it really counts, and that relationship cannot be build easily over the course of a short time.

Obito and Kakashi are basically there to be for each other as well as were rivals in more than one ways, allow them to not only compete and help each other improve, but as a measure of their growing up and reasoning for: "What it meant to be a ninja in their time how life has treated them at their young aspirating malleable age" There contradicting paths were not much less difference to that compare to what Naruto and Sasuke had in their life time, which is why Kakashi was able to learn from his own experiences and build upon it to help Naruto and Sasuke in their team effort if anything. Imo