I do think the analogy the producers might have had in mind would be something like wet shave vs. electric shave.
Did they think back in the 1960's or 1970's that by the year 2000 most men would be using electric shavers exclusively?
In this case and knowing what we do know today sonic showers might just be an option (one that Deltans possibly prefer
For TOS the problem is rather this:
The Season One crew quarter studio set had a side door possibly leading to another adjacent room (i.e. WC and shower, except for the cut scene from "The Corbomite Maneuver" where this door was part of Kirk's closet).
By Season Two they often had a corridor at this location, except for "Elaan of Troyius" (and "Mirror, Mirror").
So unless you want to see the captain take a shower with his crewmen, the turntable cubicle in the quarters would not only hold the mirror shelf and the drawers but possibly a WC and some kind of shower (darn, whatever happened to McCoy's "rank hath its privileges"...