I would prefer batteries in machine, too; but this does have some sustainability and repairability (by not needing it) advantages.
Cost is about 10x that of their non-rechargeable brethren, but obviously there's return on that investment.
I just buy rechargeable batteries and keep a charger nearby. When batteries die, they come out and straight into the charger. Always ready to go.
Realistically though if the cover for the battery is nice to remove/insert then it wouldn't surprise me if having a battery charging station and hot pairs of batteries to swap out is actually the nicer usability option vs cording or dock downtime (if you leave them sitting on the couch with a low charge then need to charge halfway through).
I doubt this would be a dealbreaker for most people, but it's a choice that will provide a consistent small annoyance for users.
I think you're mixing up the controller and headset batteries. The controllers use AA batteries and should last for potentially months of use.
The headset itself uses a rechargeable 21.6 Wh Li-ion battery with 45W charging over USB-C.
Also I would recommend switching to the IKEA rechargeable batteries which are supposedly the same thing except cheaper.