Why does GSM cause speakers to buzz?

The buzzing is AM detected signal.

The reason of audio amplifiers being hit by GSM signal is that contemporary audio semiconductor parts are actually very functional up to high GHz range. For GSM-800-900MHz range any 80mm copper trace works like 1/4 wave antenna, or stripline resonator. The signal is AM detected on any non-linearity (transistors or diode structures in chips) on multiple points of amplifier simultaneously, also including power regulator chips and so on.

It is translated into audio range as tiny but very sharp and periodic dips or pops of averaged conductivity of non-linear parts (AM detection), which are DC powered.

Think of low speed oscilloscope trace showing straight line with beads of UHF flashes. Simple sharp spikes of consumed DC current will become audible with amplifier.

In my work on hearing implants I found that the buzzing is caused by magnetic radiation from the battery wires in the phone which carry pulses of maybe 2A. This magnetic field is relatively intense and can couple into low frequency EMI susceptible circuitry of nearby devices. The noise in my case wasn't from the RF and antenna at all. This is why RF shielding may not work.

First of all, it is the power that matters in this situation. Any small speakers are going to be only a few watts, if not loss.

The power out from the handset in cell applications can be as large as 33dBm (or 2 Watts). This is the case for both UMTS and GSM; however, for GSM there are bursts that are around 217 Hz (which is in the audible range) This 2 watts of power can be very strong compared to audio signals. In UMTS, the protocol changed and was specifically designed to avoid bursts that would be in the audible range.