the Japanese do it the right way: a long soak in a hot fragrant bath and then a shower to remove the grime.
Actually, the Japanese do it the other way 'round. You wash the filth off, then you soak in the tub.
That allows a whole family to share a single draught of bath water every evening. (Bathing in Japan is an eveing ritual, not a morning one) The father always gets the first soak, while it's hottest.
In fact, when the Japanese discuss the western habit of cleaning one's self in the tub, they often use Swimming Lad's phrase:
ssoaking in your own filth.
My Japanese other half insisted that we find a home in the west that had a separate shower and bath. He was horrified at my New York apartment, which had the shower and bath in one.