I wouldn't say so much reduce output per-se, only because it isn't reducing by a significant amount wattage potential. Keep in mind that a 3db difference in SPL is either half or double the current wattage. I.E. if your amp is 50 watts and produces 100db at full bore, it will produce 97db when it is operating at 25 watts and it will produce 103db if it suddenly decides to create 100 watts. The bias shift in either bias circuit type isn't enough to significantly reduce potential output but is enough to affect the quality of life for the tube.
Biasing a cathode-biased amplifier to within a watt of the tubes rated peak spec is essentially running them in full Class - A operation. The tubes won't last very long. If you crank the amp when you play, it may pull down the bias enough to take them solidly into Class - A/B operation, but only so long as you are slamming the strings. It acts more like a compressor than anything. It is what gives cathode-biased amps that spongy, blooming, chewy, and round feeling when you play them at high volumes. The voltage drop on the HT supply also causes the rest of the amp to shift in operation too, further changing the feel of the amp.
A fixed bias amp tends to stay very firm, solid, and immediate when cranked. The HT supply still drops, so it does alter the operation for much of the preamp, but because of that HT drop, it also increases the bias for the power tubes helping to keep the sound firm and solid, adding to the amps KERAAAANG appeal.
A JTM-45 is a cathode-biased amp, even though its' circuit is similar in ways to a JCM-800, the bloom and chewiness of the JTM-45 vs. the KERANG of the JCM-800 is largely in part because of the bias circuit. But the bias shift isn't enough to appreciably increase or decrease the perceived volume level; only enough to change the feel.
