If this Logitech mouse is anything like the single AA Microsoft Bluetooth Mouse I have been using for the past 2 years (or Logitech wireless mice I own) that battery is a plus, not a minus.
Using it +8 hours a day, the AA cell consistently lasts for 3-4 months, with plenty of warning that the battery should be replaced. The long battery life is from an automatic sleep feature. While mercury-free alkaline cells are a disposal issue, they are much less so than Li-ion cells.
I'd prefer a mouse with an easily available inexpensive replaceable cell. It would be superior to a
planned non-repairable mouse with a rechargeable cell soldered to a circuit board that needs charging more frequently, along with the attendant cables or adapters with declining capacity.
The only negative I see with this new mouse is its overly complex multiple buttons and USB port for programming or wi-fi reliability. The latter may have advantage for a gamer using a very large display, but I don't need that or a plethora of buttons.