I suspect it's to do with the rhythm of the expressions -- most of us have an innate sense of what "feels" right with stress and metre -- coupled with ease of use/euphony, as HB notes.
I was thinking of this in connection with pre-decimal coinage. The coin that represented 2s 6d was known as a half crown** but in ordinary speech it was always half-a-crown** which I'm sure must be because that flows better when spoken. But had there been a coin for 1s 3d I can't believe people would have called it a quarter-a-crown, far less a quarter-of-a-crown, because they're both too lumpy as expressions to be used quickly and naturally -- instead it would have been a quarter-crown.
** for the young or non-Brits, 5 shillings (one-fourth of a pound) was known as a crown, as its origins lay in an Henrician coin which had a crown device on its obverse
*** OK, it was also called half-a-dollar, which I'd thought came from a time in the very dim and distant past when £1 was equivalent to US$4, but it might actually be older than that, since before the Union of the Crowns (ie the monarchy, not the coins) there was a Scottish dollar of the same value as a crown