During the tour time stages, I observed some riders whose bikes had a
center wheel spoke cover mounted on the rear wheel and not the front.
If not being used on both front and rear wheels, what benefit, if any,
are covers on just the rear wheel? In some cases the bikes with a
cover on the rear were using what appeared to be a carbon, 3 spoke,
aero front wheel.

Use of wheel covers raises some question about the material used and
any build up of static forces that could react to rotational motion of
the wheel that might impact the bike. For example, magnetic plate
stationary bike trainers, these use magnetic plates to generate an
opposing force between magnetic plates, causing rear wheel resistance,
causing extra force to combat resistance at the pedal crank.

Yes, I know the latter is a stretch but, it is 4:00 AM as I write this.