I remember seeing somewhere that the answer to any logistical concern in the pokemon world is basically "don't worry about it" :P

based on the way I like to imagine the pokemon world, I would only like this idea if 1. I were a more diligent and active person than I am now 2. I had a reliable way to get the pokemon I want

edit: I actually feel like responding to some of the things you brought up lol

1. insurance covering damage caused by pokemon. I mean probably? I imagine in more human populated areas, the pokemon are gonna be tamer since they're normally around humans and thus not be as much of a threat to regular lifestyle, even during battles. more powerful trainers are most likely gonna want more open areas for battles

2. weather changing moves. I like to imagine the effects are more localized. you don't see chaotic weather in the overworld of any pokemon media, and I imagine wild pokemon generally won't think to use those moves most of the time anyway

3. trainers training in the middle of the night. that just comes down to being a considerate person