A positive school culture definitely enhances the teacher-student relationship. Students feel more comfortable taking risks and participating in class when they know they won't be ridiculed for their answers, however wrong or unconventional they may be. The encouragement of curiosity and celebration of mistakes as learning points goes a long way too. This creates a feedback loop where students are spurred on to ask more questions, thereby increasing interaction with teachers.
An all-rounded education with extra-curricular activities also presents many opportunities for students to bond with their teachers outside of academic settings. These shared experiences, whether on stage or on the playing field, create lasting memories and strengthen the teacher-student bond.