Not exactly right.
When only one side band and carrier are transmitted instead of two
side bands (regular AM signal) you loose 6 db of signal recovery.
There is 3 db less power in the AM side band because of only one side
band. There is another 3 db of loss in the detector because it is not
receiving coherent signals from the audio. In double side band AM both
side bands combine in the detector to give a 6 db increase in output.

The second problem with it is that when you use a standard diode
detector in the receiver (as most AM detectors are), you can not fully
modulate the transmitter to 100% modulation or you will end up with
high distortion in the receiver.
Without both side bands in the diode detector the second harmonics
between the carrier and the one side band become very high and it
sounds distorted on high audio levels. You must keep the modulation
percentage low to avoid distortion in the receiver. With both side
bands this cancels out in the detector.

An SSB transmitter transmitting carrier and both side bands works just
as well as a plate modulated transmitter.

But some of the SSB transmitters like the Collins KWS1 did only
transmit one side band with carrier. It was easier to do as someone
else mentioned. It does sound ok if set up properly but it does not
have the quality or punch that it would have with both side bands for
the reasons mentioned above.

73
Gary k4FMX