It’s specific to alkaline batteries, not sure if expensive lithium disposables are also affected. I’ve never had a NiMH leak, whereas alkalines often do after a period of disuse, leaving a crusty mess.
And yes, my grocery and even workplace have battery recycling stations. I do use disposable CR2032, 9V or LR44 button cells as there are no rechargeable options, and CR2 or CR123 rechargeables have many compatibility issues. It’s still very wasteful annd expensive, and I tend to avoid devices using those whenever possible. I had some Bluetooth-enabled thermometers that used crackpot 2477 batteries that I eventually replaced with AAA-powered ones, for instance.
IKEA sells rebranded made-in-Japan Fujitsu AA and AAA NiMH batteries under the LADDA brand. Those are excellent, and from the original Eneloop factories before Panasonic bought Sanyo and was forced to divest the factories by antitrust authorities. Eneloops are now made in China and not as good any more. The AA is available in two capacities, I get the 2450 rather than 1900 mAh one that is like an Eneloop Pro, higher power and capacity but 500 vs 1000 cycles.
The old 1.2V NiCd AA and AAA batteries had many compatibility issues, but modern NiMH Eneloops very seldom do any more. As far as I am concerned, a device that is not compatible with them is defective by design and I will return it.