You need the blast that small because the Davy Crockett was to be fired by a human on the ground, not dropped from an airplane.
A small blast can be strategically preferable if you want to fire a bunch in a line in order to stop troops from advancing over a border for several days due to radiation hazards.
It seems that using the weapon posed massive risk for the operator, so it might have been in the maker's interest to make the bomb even smaller.
Are you sure the Davy Crocket has any lingering radiation worth worrying about? Fallout ought to be a function of radiation flux over volume, plus the unconsumed portion of the bomb, and for three stage devices the unconsumed portion of the uranium tamper as well. I seem to recall that most fallout from your typical nuclear weapons comes from the tamper - replacing the uranium with lead reduces yield by around 50%, but reduces fallout by a much larger fraction. I'd expect that after three days the blast site would be almost safe for habitation, and that you could safely travel through the site of the explosion immediately if you're in a tank or APC.
Wikipedia says that the area would be uninhabitable for up to 48 hours. The intent was not to make the border region permanently unavailable, but simply stall for time to mobilize other defensive forces.
A small blast can be strategically preferable if you want to fire a bunch in a line in order to stop troops from advancing over a border for several days due to radiation hazards.
It seems that using the weapon posed massive risk for the operator, so it might have been in the maker's interest to make the bomb even smaller.
http://en.wikipedia.org/wiki/Davy_Crockett_(nuclear_device)