And there is more friction losses with poppet valves, by definition -- you have to work against the springs, and the springs lose some energy, and there is more friction as the valve closes. Rotary valves have spherical moving parts and if they are precisely fitted, they will have much lower losses.
Judging by this animation:
http://www.coatesengine.com/rotary_motor.html
The piston needs to be domed and possibly made to fit into the recesses of the valves? It might be that the valves could be cylinders; instead of truncated spheres? This would shrink the space about the piston at TDC, I think.