With C-bias, the voltage on the cathode actually 'subtracts' from the voltage available on the plate, because the bottom of the cathode resistor is referenced/anchored at GROUND. A little less Vp means a little less plate voltage "swing" and thus a little less power output.
If, however, the B+ is increased exactly the same as the Vk voltage, then there would be no loss in power output, but there certainly would be a drop in power utilization efficiency (Po/Pi) because now MORE B+ had to be used to create the same power output...thus, efficiency went down ↓ .
Go back to the first equation, Po ≈ (Zoo/4)*(gm*Vg)^2, and plug-in 6KΩ and you'll see that reducing the OT from 8KΩ to 6KΩ will cut power to about 16-17W...a 25% reduction.
The closer the power tubes are biased to Class-B operation, the more "cross-over" distortion becomes a problem.