A guy named John Carson developed SSB at Bell Labs in 1915.
John Renshaw Carson. Yep, he also is famous for Carson's Rule which describes the bandwidth of an FM signal; BW = 2fm +2dK.
A quote from Wikipedia:
"At AT&T Carson was involved in early radio telephone experiments. In 1915 he invented[1] single-sideband modulation to transmit multiple telephone calls simultaneously on a single electrical circuit, and was responsible for installing the first such system between Pittsburgh and Baltimore. In 1922 he published a mathematical treatment of frequency modulation (FM), which introduced the Carson bandwidth rule. In his 1922 paper, Carson presented a negative opinion of narrowband FM, which occurs when the maximum frequency swing is made narrower than the audio bandwidth. Later, Edwin Armstrong managed to demonstrate that FM can be advantageous if the frequency swing is significantly wider than the audio bandwidth. "
Ironically today's 2-way nbfm communications is moving to even less deviation to decrease bandwidth so more channels can be packed in to the existing 2-way bands.
Weak Fm is inferior to weak AM signals with respect to S/N ratio but the FM S/N quickly increases over AM as the signal gets stronger.