You misunderstand modern (post 1950) SW transmitter design.

Class-B, PDM and PSM (and hybrids of the two) modulators produce an AM
waveform, no matter what.

Some Russian Class-B transmitters can handle transmitting FM, but these are
very pure analog beasts.

Only the modern PDM / PSM / Hybrid transmitters are being put into service
for DRM, no Class-B modulators.

CODFM (as DRM uses it) in the SW bands is a PSUDO-CODFM; the audio of the
CODFM signal is imposed on an AM waveform for transmission. The BSEE
electronics is a lot simpler, and it is backwardly compatible with the
installed base.

Thankfully this DRM AM-CODFM design is so simple that it is totally
misunderstood, and you can't tell the difference at the receiver end.

PSUDO-CODFM aka AM-CODFM
-- CODFM signal is of Audio bandwidth, 10 kHz or 20 kHz
-- Most modern SW transmitters can accept 20 kHz audio with only minor
retrofits
-- Most modern SW transmitters are "linear" up to about 40 kHz, based on 90
kHz PDM / PSM clock rates
-- Most modern SW transmitters only know how to transmit AM +SSB (but not
FM)
-- SW DRM transmitters universally get their PDM / PSM clock rates increased
to 100 kHz + (Continental, retrofit infos)
-- A true wideband CODFM signal of 1 MHz would not work on SW, ITU
allocation issues aside ... the installed transmitters base cannot handle
it, only PSUDO-CODFM is workable
-- VHF / UHF CODFM transmitters are real CODFM transmitters, as there is no
PDM / PSM / etc involved.

There are no true CODFM transmitters in the SW band with powers above 2kw
(or maybe 10kw), as the electrical engineering is just too hard to do.

DRM,
the new standard for DAB over SW uses AM modulation with CODFM content.
=======
DRM, Digital Radio Mondiale, uses COFDM, as does the European VHF and L-band
DAB system and the US HD Radio. COFDM, in its multiple subcarriers, does not
use AM. Instead, each subcarrier is modulated with an orthogonal QAM. So
that's a modulation in which both amplitude and phase are varied at the same
time, to carry twice as much information as an AM signal of the same
bandwidth can carry.