And they'd be absolutely blind without GA. There's no magic window into customer behavior. If you were actually in a physical store then they could look at you through the cameras. This way they can know if there are basic problems with the store.
With a website, they would have absolutely zero way to know what your experience of shopping there is like without a tool like GA. The only data they would have at all is sales numbers. The experience of shopping online would be immeasurably worse without it.