Well, a funny picture came to mind as this question popped into my head. Why in the world do we call it drag racing? Surely, it has nothing to do with transvestites racing, does it? Maybe a little closer to the target, could drag refer to "smokin’ "?
Gosh, isn’t it hard to run in those stelleto high heels!? 
Drag can mean street or road.
Here’s the NRHA website, read all about it.
Now that site has to do with car drag racing. I did see a different kind of drag race in Key West where drag queens raced down Duval street on foot in high heels, but that’s a different subject altogether … LOL 
From nhra.com —
About the term “drag racing”
Although the tiretracks of its history are clear, the origin of the term “drag racing” is not. The theories are almost as many and varied as the machines that have populated its ranks for five decades. Explanations range from a simple challenge (“Drag your car out of the garage and race me!”) to geographical locale (the “main drag” was a city’s main street, often the only one wide enough to accommodate two vehicles), to the mechanical (to “drag” the gears meant to hold the transmission in gear longer than normal).
[cite-free comment from lazy person with no patience for server speeds tonight] The term “drag” was used to mean a street or throughway before the arrival of the automobile. It goes back to the Civil War, at least.[/cite-free comment from person with no patience for server speeds tonight]
The OP sounds like the intro to a bad Seinfeld routine.
"Why do they call it ‘drag racing’? The drivers aren’t in drag. The car isn’t wearing a dress. The track isn’t lined with practical pumps. What’s the deal with that?
Some of these guys should drop by a 50% off sale at a Lower East Side boutique. They’ll see some real drag racing…"
I’m sorry, so sorry, I couldn’t resist…
SNL.
Eric Idle in corset, garter belt, stockings and high heels vs. Dan Ackroyd in corset, garter belt, stockings and high heels.
Drag racing.
Funny.