I learned a bit about DRM broadcasting on HF band recently. I don't think it will succeed in replacing AM shortwave broadcast.
DRM is a digital broadcast scheme. It features 16/64QAM, OFDM, xHE-AAC. A DRM station usually takes up 10kHz bandwidth in HF band. It may carrier one audio program and some auxiliary data (text, program guide, emergency warning, etc).
Analog AM is good enough for voice. DRM can provide FM radio like audio quality on shortwave band. However, most shortwave stations are operated by governments (e.g. BBC, VOA, CRI) or religious groups (e.g. FEBC). They usually have voice programs. AM's ~4kHz audio bandwidth is good enough for this use case. Another use case for shortwave radio is emergency. Analog modulation also works well for this purpose.
Complexity and cost. An analog AM receiver simply need LO, mixer, filters, envelop detector, audio amplifier. A DRM receiver must have a DSP that can demodulate OFDM, a xHE-AAC decoder, and a micro-controller. All these adds to the cost and power consumption of DRM receivers. I could not find any DRM receiver for less than 1000 CNY in China. I tried listening to DRM on SDR, the effort is not trivial. I also experimented with the CML DRM1000 module, which I do not recommend.
Lastly, mass media broadcasting itself is going downhill IMO. The mobile Internet is capable of carrying high quality audio and video streams from independent "creators". I have not subscribed to cable TV for years.