I own multiple bikes and commuted for (about 25) years. Personally, I found the English 3 speeds very comfortable for commuting and errands, and used them for club rides also. I'll admit this worked for me but none of the other club riders tried ths. My commute was a bit shorter than yours, maybe 15-18 miles round trip, depending on errands.
I found having additional bikes useful for several reasons:
Backups if one bike needed repairs - I had space to store them, so I could wait until weekends if I needed to make repairs
Weather - with snow, ice and rain, a MTB had much better (cantilever) brakes than 40 year old 3 speeds. Studded tires are also much better on ice.
Guests - extra bikes are convenient for visiting friends without bikes, especially folding bikes
In the unlikely case that your current bike is more recreational and doesn't yet suit your transportation needs, feel free to make changes (fenders, etc.).
Get another bike if you enjoy it; if you're commuting 20 miles daily I'm sure your current bike will be fine for anything short of 300 mile randonneuring tours.