Tbh I never understood why Jiraiya didn't just like. Take the Ame Orphans back to Konoha while he trained em, and then sent em back off to Ame when they were done like??? Jiraiya what???? Were you thinkin? Get your shit together man your team mates and village need you probably more than three miserable kids (one[??] of them an Uzumaki!!!! Hello!!!) have to stay in a country that likely wants them dead, when they can train somewhere safer and then come back for a Revolution™
LOGIC. I agree, tbh, though I can see the three kids being really wary about going back to Konoha too. Still, they went to a Konoha nin for training, so actually following him back to a village with access to more teachers and lots of food and actual safety seems like it would have been a better bet. Also, no village desertion on Jiraiya’s part. That likely would have been better.