https://www.diffen.com/difference/AM_vs_FM
Even if you multiplexed all possible amplitudes into one it still wouldn't be worth it for (two-way) digital communications.
AM band uses a large frequency range, 530-1700 kHz, but the total bandwidth is small, slightly more than 1MHz.
Telephone is bad compared to AM and really bad compared to FM or CDs. Human voice fits in much smaller bandwidth than music.
That's part and parcel of station management's programming decisions for HD Radio subchannels on the AM band, hence the focus on ''talk''.
edit: wasn't too clear that I meant to say that the 1200 bps must be from an old standard
56K modems also had the advantage that the noise floor for the downstream direction was much lower than the upstream direction.
Wouldn't it be better to repurpose those frequencies for country wide digital broadcast that could also send other data during emergency situations?