Technically, and I really don't mean this to sound pedantic or smart - some A320s have "Spin Brakes" on the nosewheels. That is, friction brakes in the top of the NLG Bay that stop the nosewheel spin on retraction. I don't know if it was abandoned on later production aircraft, but there is an optional SB to remove them as they were deemed not necessary.
As an aside, the B727 is the only aircraft I have encountered with actual brakes on the nosewheels, are there any others?