2 minutes is way too long. My mouse stops working in the middle of an intense flow? When I'm rushing a piece of work for a deadline? When I'm in the middle of a game? Stopping for 10 seconds to scramble to get the cable in is fine. Sitting on my hands for 2 minutes waiting for the thing to charge, during which my machine is essentially unusable is totally unacceptable.
Why not put the port on the front (like Logitech does)? It can still be placed aesthetically - the front side of a mouse is something you never ever see.