I can’t believe this flight school does training out over open water like that. As a pilot from the Midwest I actively fly around the Great Lakes in light piston engine aircraft, even in the summer.
Now compared to over land, you can easily land a small piston engine plane just about anywhere. Highways, large parking lots, open fields, all become acceptable landing spots. In a Cessna 172 which is commonly used for flight training, impact speed can be as slow as 45 knots. Even a crash into a dense forest is survivable with some luck.
I guess I’m just not familiar enough with LA airspace to fully appreciate the lack of space for training flights. I’ve been in and out of LAX and it is busy no doubt. I just haven’t done GA operations in that area so I wasn’t all that familiar with all of the additional airports and traffic.
Personally, my pucker factor would be exceptionally high practicing stalls, or multi-engine training with engine shutdowns and Vmc demos over open water. Regardless of the temperature.