Is axle cone pitting more common on rear drive side? I finally got into the rear hub of my new-used bike and found one cone pitted, the drive-side cone only.  The other three cones are fine.

I happen to have also picked up a second, compatible bike from a neighbor who was throwing it away.  Lucky me; I've rescued a lot of good stuff off of it.  I thought I'd use the corresponding cone from that one, but that turned out to have pitting too.  And the other three cones there are fine.

Is this a common thing, maybe because of the chain pulling on that side?
The rear wheel carries the most weight, so straight off its subject to 60% of the stresses where the front only carries ~40%.

Rear axle takes drive from the chain, which is on the right hand side.  As the power comes from the chain via the cassette, that side of the axle is pulled forward.  Any microscopic slack will allow a bit of movement.  When the axle moves, the left side (NDS) is more likely to seat better merely because its not on the drive side.

So you have movement, which is a sure fire way to make your ball bearings unhappy.  This leads to hot or glazed bearings, and damage to the cone.

In addition this is in the middle of the cassette, which is probably the dirtiest place on your bike.  There's always some powdered grit or oil or something, and the tiniest movement of the axle will allow contaminants into the bearing which exacerbates damage.

Short answer: Yes.  The DS cup and cone suffers damage faster when not properly maintained.  Check your nut tension whenever the wheel is off the bike.

When adjusting wheel bearings, the rear should be pre-loaded just a little.  That means just a tiny bit "too tight" when compared to a front axle.  Not so tight it doesn't roll, but just enough to apply some constant pressure on all the balls, not just the ones at the top of the race.

Finally, be happy because cones are relatively cheap.   Take the old cone into a LBS and ask for one like that.  Depending on sizes, you could be looking at anything from $1 to $20.   On beater bikes, I've sometimes found a whole rear axle set works out cheaper, and gives me a known unbent axle as spare.

Do buy new ball bearings too, its false economy to rebuild on old balls.