Do you not read the manga? Madara planned the whole thing. He targeted Obito specifically. Madara himself said he "waited for when minato was on another mission". It doesn't matter of minato was there that day or not. Madara would've still done all those things the minute mintoo wasn't with them. Minato isn't their father, so he can't watch them 24/7. It was an unavoidable situation.Minato had to part from his squad to fulfill his obligations during the war. I get that. The problem is the same tragic event happened again. Rin gets kidnapped, but this time she gets killed. By Kakashi. After the Hidden Mist ninja make her the Three Tails' jinchūriki.
You would think after losing one member of his squad Minato would realize that leaving young ninja (even with one them being a jonin) alone is bad idea during a time of war, and he would maybe retire from being a sensei so could focus on other duties, because trying to do both is obviously impossible. But nope. He leaves his squad again, and another member dies.
I'm not knocking Minato's ability and or his character, I'm just saying the guy was a crappy sensei.
Please use some common sense, Minato is not duty bound to be their supervisor after they became Chunins and they were all Chunin's with Kakashi being a Jounin in the events you mentioned. Chunin's need to have a grown up mentailty, that's why Shikamaru was made Chunin over Naruto, Neji, and Sasuke. Minato had them as students for years but only because he was still teamed up with his team but he's not duty bound to always be with them. At Chunin level you can become teachers for Genins, go on missions yourself, and even be a team leader. They were in a time of war so instead of having their strongest ninja babysit his students who are Chunins+, they needed him to help fight on the battlefield.I'm sure he was good Hokage and husband and all that, but as a sensei he was straight up horrible. He was never around for one. All the traumatic events that Kakashi and Obito went through occured because Minato was off doing something else, which kinda eliminates the point of being a sensei of a team of young ninja. He just kept assumed that Kakashi and Obito would work out their problems, but they didn't. He just assumed that his team would be fine on their own, but they weren't. And despite already losing Obito due to negligence, he left his team alone again and lost Rin too!
Obito getting crushed and being found by Madara, Obito witnessing Kakashi having to kill Rin, Obito unleashing Kurama on the Hidden Leaf, Obito starting the Fourth Ninja War and trying to Infinite Tsukuyomi the world with Madara - all of this is pretty Minato's fault for being irresponsible.
Even Orochimaru was a better teacher than Minato was.