A carrier plus one sideband can sound very good:
witness the CHU time signals at 7335 KHz. (USB + carrier).

That "A.M. Equivalent" mode used to be denoted as A3H,
whilst SSB (no carrier) was A3J and standard A.M. was A3.
(The official nomenclature describing the modulation modes
has become more complicated.)

Someone listening with a 6 KHz IF bandwidth receiver
with envelope detector will hear a bit less recovered audio
from an "A.M. equivalent" transmitter than from
a standard A.M. transmitter,
as if there were a smaller percentage of modulation.

Someone listening with a 3 KHz wide receiver would not notice
the difference between A.M. equivalent and standard A.M.,
because his receiver is in effect converting all sgnals
to A.M. equivalent. One difference: he wouldn't be able to switch
sidebands to dodge QRM.

Regards,
Ed Knobloch