As others have stated amplitude modulation is indeed used for digital modulation.
However, the biggest issue with AM modulation is that you are using a natural phenomenon, the envelope variation, to carry your signal. That means your signal is highly susceptible to interference by outside causes, eg. neighboring frequency transmitters, variability in local field strength, solar effects etc etc.
That's why your AM radio stations sound so much worse, with a ton of "static", compared to your FM stations.
For transmitting the latest Mariah Carey song AM is acceptable, but if you want your 1000 page document to arrive without any errors.. that is a different story.
You CAN use AM to transmit digital information, however, in order to have zero errors, the transmission rate needs to be much slower compared to the likes of FM.