The reason is because if you are greatly concerned about aerodynamic drag, you can get a recumbent that has way less frontal area than an upright bike. No fairing can really make up for the upright bike's larger frontal area, and the tall profile makes them susceptible to crosswinds in regular use.

Last time I looked--Zzipper and Windwrap both make small fairings that you can mount on the handlebars of an upright bike, if you wanted.

The info from Bicycling Science may be technically correct but it seems rather outdated.
The Vector trikes and Avatar Bluebell bikes date from the mid-1980's; they look pretty slick but both of them are roughly 30 years old. I don't know what their drag numbers are but I'm pretty sure that they would both be totally uncompetitive today.
The Varna Diablo was probably the fastest direct-sight recumbent bike, before the camera bikes took over.

In years past there were Battle Mountain teams that ran faired upright bicycles.
There was also one team that showed up a few times with a fully-faired folding bicycle.
Neither of them went anywhere as fast as the faired recumbents did, but they still went way faster than an unfaired bike of the same type could.

You might ask on the recumbents.com website if anyone has more info on either of these. That site is fairly small but does seem to have a lot of IHPVA/Battle Mountain regular attendees.