How come people connect their arduinos to buzzers without any coil protection?
That kind of "buzzer" doesn't have a coil.  It is a "Piezo Transducer" and uses a crystal to produce the sound.

When you're using a real speaker and producing sound you are doing it very differently to switching a motor or a relay on and off.  You're generating a much smoother waveform and you don't have the sharp "ON-OFF" that causes a collapse of the magnetic field.  You're actually gradually reducing the power and then reversing it to remove the magnetic field then apply a new one in the opposite direction (if you have wired it right of course).

Also the currents involved in driving a speaker like that are minuscule compared to switching a relay, especially when driven direct from the Arduino.  For louder volumes you will use an amplifier, and that deals with the whole protection within itself since it is designed to drive a speaker.