I think it is more than that, the shower is a proper refuge where external stimuli is severely limited. Sounds are limited by the running water, temperature is controlled by the water, visuals are limited, and no one is generally barging in.
When I was studying math at University I had a remarkable number of eureka moments in the shower where suddenly infinity made sense. Smart phones didn’t really exist then but showers still held power as a great place to think
my experience studying math was the same, so many concepts clicked when i was in the shower. a bit later on, a lot of the eureka moments in research projects happened in the shower too. i’ve wondered how common it is in other fields to be doing a considerable chunk of the research in the shower.
After finishing up calculus and differential equations taking real analysis was a trip! Basically opening up the box that is calculus and seeing why taking the derivative of a function means dropping the exponent and so much more. It frequently dealt with infinity and we went from writing long equations to solving word problems involving infinite doors. It was great
