DB you are correct about thickness being the critical dimension.

There is also more to the story --- in the case of model aircraft, & for a given thickness, plan form, section taper & aspect ratio, flat bottomed wings are inherently faster than symetrical or semi-symetrical wings. They provide the necessary lift to support the model at a lower angle of attack & require less nose-up trim force than is required for a sym or semi-sym airfoil. In some cases, flat bottomed airfoils can actually provide all the necessary lift at zero AOA, or even 1 or 2 deg of negative AOA, depending on speed. Fully sym sections are the worst choice for speed, as they require a significant AOA to provide adequate lift & require substantial nose-up trim forces.

Trainer wings are usually slow because they have a large span, have a low aspect ratio, a large wetted area & are often relatively thick -- none of that has to do with the airfoil section