I think the solutions that will work best to reduce the usage of generative AI by students are dependent on the group of learners you are working with. As an elementary teacher, I feel that the best strategies are those that ensure class questions includes connection to self or the world. Typically, my younger students are not going to be able to do the higher level thinking required to get generative AI to complete a sensical response to a question like this.
However, if you were a high school AP teacher, your students would be more likely able to utilize generative AI to build answers to complex questions. For this group, frequent, low stakes assessments may be a better direction to go in because the students in these classes are likely driven by success. If they feel they will not be able to achieve their desired score without the use of AI, they may be more likely to cheat. Lowering the stress and pressure may prevent their use of AI.
In determining what strategies will help prevent the misuse of AI within your classroom setting, I think it is important to investigate the motivation of your group. Why are they inclined to use AI, and then pick an appropriate mitigation strategy based on that discovery.