On one hand, it could increase student engagement and motivation if they have a teacher whose teaching style or personality resonates with them. A better student-teacher relationship might lead to improved academic performance and a more positive learning environment. It could also empower students and give them a voice in their education.
However, there are significant downsides. Children might base their choices on superficial factors rather than pedagogical skill or subject matter expertise. Popularity contests could lead to some teachers being overwhelmed with students while others are left with none. This could also create unfairness and potentially disadvantage students who don't get their preferred teacher. Furthermore, it might undermine the authority and professionalism of teachers, and lead to logistical nightmares for school administration. Finally, a child's preference might not align with their educational needs.
Ultimately, while the idea has some appeal, the practical challenges and potential for negative consequences are substantial. A more balanced approach might involve giving students more input into their learning experience through other means, such as elective choices or student feedback mechanisms, without giving them complete control over teacher selection.