The average commute time by bicycle, assuming you were going that 15-16 mph the entire time (which you won't be), would be an hour. You forgot to factor in climate when you talked about whether or not people would trade in their cars for bikes. When it's over 100 degrees outside, and humid, with a high chance of rain in the afternoon... people don't really like to bike to work. When it's freezing, snowy, and there's a high chance of ice... people don't really like to bike to work. When it's raining all day... people don't really like to bike to work. When they work somewhere that requires the transportation of equipment to and from work with them everyday (laptop, briefcase, suit jacket, dress shoes)... people don't really like to bike to work.
Add in the "culture of driving" in the US, and I still stand by my assertion that the bulk of the populace will not suddenly switch to biking to work, or for that matter to get groceries, take their kids places, take roadtrips, etc..