I still have and use an Apple branded AA chargers (came with Eneloops in Apple livery). It has the same connection system as the external chargers so I normally have it connected to a long cable. Used it internationally with the same adaptors as for my MacBook charger.
Received a refurbed Mac and someone had swapped out their mouse for my rechargeable one... always a song and dance to re-connect every time the batteries die. (I pretty much use another mouse to get to the Bluetooth icon on the menu, I'm no Mac expert.)
I always shake my fist in the air and curse "Eric Seifert's Mouse" semi-silently in frustration!
The reason for the thinness of the Apple Mouse is so that gestures can be used on the top like a trackpad. If it were domes like a typical Logitech mouse, you couldn’t do that. Whether those gestures turned out to be useful is another question but that was the reason.
I imagine they also wanted to make 1 mouse ambidextrous. Maybe they should just tilt it and ask the user to choose handedness. I use a track ball and split keyboard and it has never been an issue no one can use my setup except me.
The constant need to have lithium ion is really terrible. Battery life is less of an issue when I can swap batteries quickly with common sizes.
Do you use an Apple mouse? It's not like you are frequently charging. Just plug it in while you go get a coffee or lunch and you are good for weeks. It displays a low charge warning in the menubar to alert you.
I found having to always keep a supply of batteries at hand was more inconvenient than just plugging in the mouse once in a while.
I have a 2xAA Magic Mouse that I still use occasionally. Feels a little heavier than the later models, can't tell them apart otherwise without looking at the bottom.
The obvious response is that the mouse should be thicker to accommodate those batteries, but that goes against Apple's entire ethos.