I believe you are discounting the fact that a shower is not always available at the place you are going. Take for example, you need to go to a job interview. I skip the shower at home, bike to the job interview, sweat profusely during the ride, and now I shower where exactly?
What about needing to go multiple places during the day? Should I now shower 4 times because I have 4 stops that require me to interface with people and appear clean?
Biking in Florida (substitute most of the southern US) for 7-8 months of the year is simply not possible unless it is acceptable to be a sweaty mess at each destination.