Why should BJTs be saturated in switching circuits?
There is a third reason, related to your reason #2: Because the voltage across the BJT is low, its power dissipation is also low.
This point was driven home for me many years ago when I was building a variable DC power supply1 with current limit. A transistor switched on a lamp2 when the current limit was engaged. When I was testing it, I deliberately overloaded it, the lamp started to light up, and the transistor promptly caught on fire!3 I soon realized that I had failed to saturate the transistor, and its power dissipation was far too high as a result.

1 723-based, which gives you an idea of just how many years we're talking about...
2 28-volt incandescent, not a wimpy LED!
3 I still have the scorch mark on my breadboard socket.