I have towed gliders in Cessna's and tailwheels, I strongly prefer doing it in a taildragger. I've towed CAP cadets before, and CAP is probably better off finding glider clubs to do tows for them. The clubs just have more expertise, since they are doing it more.
The biggest reason for using a taildragger is prop clearance. The glider is in the air well before the towplane is, and whatever that glider does moves the towplane. If it gets too high on tow when the tug is still on the ground, I really don't want a prop strike. Way less likely with a taildragger. Aerotow from turf is fairly common, and taildraggers are just better suited to the grass.
All around, the Pawnee is the best airplane to use for glider tows. Gains altitude faster, which builds in a lot more safety margin for the tow pilot. Better climb rate also means better efficiency - more tows per hour. And it takes some effort to ground loop the Pawnee (it has been done, but not common).