Please someone tell me Is this a good analogy for Agile vs. Waterfall.
I don’t think this is a good example. Going to school every day is quite a repetitive task that typically will benefit from a waterfall approach over time.
While the described disaster scenario may happen it is highly unlikely. When it happens it will affect “agilist” and “waterfallist” in the same way (the planning does not have to be extremaly time consuming). Waterfall works well in such repetitive scenarios when you can have prescribed procedures and best practices based on previous experiences. For example, when checking the weather you can decide to either take a walk, take a bike, drive a car or use a public transport. You can fine-tune your speed to hit a green light at every intersection, you can select train doors that will more likely allow finding a free seat etc. All those ideas will become a part of a procedure, a waterfall of events designed to optimize the time of a repetitive task.
On the other hand - planing the first trip to school may be a better example. You may want to try different ideas before selecting most effective one. Waterfall in such case would be to plan all possible scenarios before even trying one, that may be satisfying or may lead to a wrong address, rendering all other planned routes useless.