It is not uncommon to for some guitarists to use partially depleted batteries to power certain effect pedals, especially fuzz pedals. People can get particular about tracking down specific brands of carbon-zinc type batteries that are perceived to have preferred discharge characteristics. And there are “battery sag simulator” pedals.
https://danelectro.com/product/1960s-vintage-battery/
https://jhspedals.info/products/volture?srsltid=AU7gw4VF4W_4...