The receivers used for FM and AM are different. In transistor radio, both the receivers are present but in mobile phones, we only have FM receiver. There could be many reasons for not including an AM receiver in mobile phones. Since most of the FM stations are run by private companies, the entertainment quotient will be more in FM as compared to AM, which is generally run by Government. The other reason for not including AM receivers could be requirement of extra circuitry, which may increase the cost of the mobile phones. In addition to that AM signals are more prone to disturbances when compared FM signals.
The disturbances that we hear in FM radios while traveling could be due to weak signals or due to receiving of the same signals multiple times because of reflections from the surrounding buildings.