Highly cambered airfoils like the Seligs and Epplers are hardly ever used in propeller or wing sections. Why?
Does their performance reduce at high Re? Are they only adequate at low Mach, low Re?
The question only regards the aerodynamics. Ignore fuel storage and structural elements.
First propeller use: A highly cambered airfoil would cause high pitching moments and twist the propeller blade. Of course you can pre-twist the blade so it will assume the correct shape in the desired operating point, but a propeller needs to work over a wide range of operating points, from take-off roll to high speed flight at altitude. In off-design points (i.e., most of the time) the propeller would have poor performance when compared with one which tolerates more diverse conditions.
Note that indeed thin, highly cambered airfoils are used on compressors and turbines in jet engines. Those are more stubby and enjoy much narrower variations in flow conditions, so the highly cambered, thin airfoil is indeed the best choice here.
Use on wings: Some aircraft do indeed use highly cambered airfoils. Those with low maximum speed like human powered or electric propulsion aircraft prefer those airfoils because they create the needed lift at the lowest possible speed, so the aircraft can fly with the limited installed power. As soon as the aircraft needs to cover a wider speed range, however, a lower camber is needed to keep drag low at high speed. This is similar to the use on propellers: A wider operating range requires to move away from the narrow optimum offered by those highly cambered airfoils.
Note that aircraft with a high wing loading use extensive and extensible high lift devices which turn their wings into thin, highly cambered structures for landing. Again, as soon as a lot of lift at low speed is needed, thin, highly cambered airfoils are the best choice. Adding slots between segments will make those work even better than a solid airfoil and allow to use more camber.
You can't just cherry-pick aerodynamics and exclude everything else when it comes to aircraft design. But let's entertain flight dynamics alone for this instance, and use Selig S1210 or S1223 as examples.
Selig-S1210 (for Re 0.2e6, 0.5e6 and 1.0e6) characteristics:
First, notice that the linear range of the airfoil extends from $C_l$ 0.5 to 1.9, which means that this airfoil is only suitable for low speed flight.
Second, the maneuverability of such a wing would be questionable. For a typical aircraft, we would need the ability to do at least a 0G push-over and a 2G pull-up (for Part 23 and 25 aircraft). However, the airfoil is clearly stalled before reaching $C_l$ of 0; and if we use $C_l$ 1.0 as design cruise lift coefficient, then 2G pull-up would also be difficult.
Therefore, while such high lift airfoil may serve niche applications such as high lift competitions with model airplanes, its aerodynamic utility is limited.
