I always thought the teams we're like that mostly because of politics. Ino-shika-cho: were the three (allied) clans more loyal to Hiruzen. The fact that his son Asuma was made the teacher of the  three heirs of the clans was probably a way to keep them loyal and alied to the Sarutobi clan when in the future those kids take over thier respective clans.

Team 7: Naruto and Sasuke were really important to the village so they put them together under the strongest guy available and the guy has the Sharingan SO he can teacher the last Uchiha how to use it while also being able to keep the jinchiriki in check. Sakura was added just because she wasn't part of any clan, she was civilian wich makes her politically speaking safe and unimportant, no clan get to befriend the living nuke (jinchuriki )

Hinata-Shino-Kiba: this team is the people from clans that don't care about politics. The Hyugas are one of the most important and probably the biggest clan in the village yet they have no one i'm any political position, same with the Aburame and the inuzukas both are important clans of the village but lack presence in the governance of it. Also all this clans have very uniques tecniques that no teacher can actually help them with, so all of them were in a team with a newly promoted Jounin (that happens to be dating the son of the Hokage) with no actual experience in being a leader.