"Half a foot" vs "A half foot"

Right around 8:30 this morning, the new weathergirl on Good Morning America said "about half a foot of snow".

She got it right! "Half a foot" instead of what they always say, "uh half foot".

She's the only one. The rest of em always say it wrong. And not just about the weather. It's "uh half inch" instead of "half an inch". It's "uh half mile" instead of "half a mile". It's everywhere, and all the time -- or "always and everywhere", to use Friedman's phrase. And it is wrong.

THERE IS NO SUCH UNIT OF MEASUREMENT AS THE HALF FOOT.
THERE IS NO SUCH UNIT OF MEASUREMENT AS THE HALF INCH.
THERE IS NO SUCH UNIT OF MEASUREMENT AS THE HALF MILE.

THE UNITS ARE THE FOOT, THE INCH, AND THE MILE.

But ignorance is bliss, and my complaint will no doubt fall on deaf ears.