Modern wireless mice from logitech and microsoft last for a year or two on a pair of aa batteries. There is no point making them rechargeable any more. You can always use rechargeable aa nihms if you really want to, but personally I just have 50p of alkaline aa's and in two years I will have to change them again. Some things do get better :)
The only point IMHO to built in battery, is if it very convenient to recharge, which is not the case.
I have an HHKB which uses 2 AAA, with rechargeable Li batteries which I can reload with usb, while still using the keyboard with cable (once every 6 months or so)