I was thinking about why all the DADA teachers stop after a year and Moody didn't really make sense. I mean obviously, Crouch Jr. couldn't keep teaching, but there wasn't a real reason given for why Moody didn't start teaching like he was supposed to after they found him. Given that Umbridge replaced him, I guess the Ministry insisted or Moody didn't actually want to and Crouch initially accepted the job disguised as Moody when Dumbledore asked him, but is it ever actually stated what happened?
Not really, if anything he had less time. When they found him, it was the end of the school year, so he wouldn't have had all summer to start teaching again. In the Summer, he helped escort Harry to Sirius's house about a month(?) into Summer. I guess he would have had to make lesson plans or whatever over the Summer, but I doubt that's as stressful as doing missions for the order. Though the theory that he's more useful as an Auror than a teacher makes sense too.