With shortwave broadcasting [where your carrier can almost vanish but the
sidelobes may remain relatively intact for PLL or SYNC detection] ...
throwing away the sideband has had mixed success for the international
broadcasting sector. International broadcasters tried "compatible SSB" (in
the 1990s) and it did not work.

SSB is used by hams and military in the shortwave bands for 1 and 2 hop
voice communications (and 3 or 4 hops for data)... but using AM in its place
would make for better multihop communications systems in the HF region. DRM,
the new standard for DAB over SW uses AM modulation with CODFM content. DRM
may kill off the hundreds of SSB based digital [RTTY] transmission systems
used in the HF bands.

In my view, having a carrier that is 1.5db stronger than the rest of the
signal would work for 8VSB (in UHF and VHF TV service) ... but I would never
agree with getting rid of the sideband entirely. SSB (with no sideband) may
be spectrally efficient ... but horribly expensive to decode. I don't know
if the ATSC spec supports a stronger carrier, and there is the issue of the
"DC" component inserted into the 8VSB signal 7% of the time to allow
decoders an opportunity to latch onto an unmodulated carrier for PLL or SYNC
decoding.

In summary 300 kHz for a sideband is a small spectral price to pay for ~19.5
mbs link that does not lose sync so easily.

How wide is the 8VSB lower sideband?
http://www.broadcast.net/~sbe1/8vsb/8vsb.htm

The (mostly suppressed) carrier is 310KHz into the channel in most cases.
I haven't thoroughly studied the standard but I believe almost all of the
310KHz below the carrier is used for lower sideband. (i.e., the LSB
extends nearly to the bottom of the channel, making the sideband 310KHz
wide)

Can't say I'm entirely sure why they bother with a lower sideband at all.