Because the total swing is what matters. So here is how a differential output amplifier using this bridge tied load approach works. Take two identical push pull amps (as an example). Each has 75 volt rails. For the sake of argument, you have 10 amps of current from the power supply. That is 1500 watts based on the swing between +/-75 volts (150 volts), but we need to divide by 1.41 to get to RMS. Class AB would only be 65% efficient. Class D would be 90% efficient. Let's go with Class AB. Now we are down to 975 watts peak and 691.5 watts RMS and that would be pushing things pretty hard. Now we go to a bridge tied load version, the second amp is inverted (phase is reversed. You tied the positive terminal of the second amp to the negative terminal of first amp. That is now referenced to ground. It doesn't touch the speaker. The positive terminal of the first amp goes to the positive terminal of the speaker. The negative terminal of the second amp goes to the negative terminal of the speaker. Again, no ground connection here. The two swing between these amps is now going to be much higher, 300 volts, like having one amp with +/-150 volts. Now we have basically 1300 watts of RMS power output ability. Or...you could go down to 35 volt rails, now the caps are very small and way cheaper/way more reliable.
Here is a schematic of one of the older SDA speakers:
View attachment 46434
Basically it is pulling the sound information from just the positive terminal, which on a single ended output amplifier, is fine, all of the signal is present on the positive terminal of a single ended output amplifier.
View attachment 46435
Here is a PP amplifier. You can see there is a positive output, load, ground. All the signal is on the output here.
But a differential amplifier is different.
View attachment 46436
Half the signal is on the + output, half is on the - output. Go back to the rail voltage comment. To obtain the total swing, the sinewave isn't swinging up and down the full amount on just the positive output. Instead, half the voltage level is on the positive terminal and half is on the negative terminal, with inverted phase. That is what gives the total voltage swing. So for a given wattage of output, the stereo array speakers would only see half the voltage swing that the main drivers see, thus 6dB quieter.
Does it make sense now?