Why does the chevron-shaped engine suffer losses in thrust performance?
The chevrons need a small pressure difference between the fan flow and the surrounding air. Then they will work like small delta wings and create two strong vortices per triangle, which will help to mix fan flow and outer flow. This mixing is responsible for the reduced noise, because it will distribute the kinetic energy of the fan flow over a bigger mass of air.

This mixing by itself uses up some of the energy of the fan flow, and thrust is produced by the conversion of the pressure increase due to the fan into kinetic energy. With the chevrons, a little of this kinetic energy is now spent for mixing and cannot contribute to thrust anymore. Hence the reduced efficiency.

You're right to assume that less sound should mean more thrust. In fact, the sound energy is not evenly distributed over all frequencies, and by adding some noise at frequencies with low noise contribution, the peaks at the lower frequencies which contain most of the noise can be lowered.