Why is speed not normally used to control the armature voltage of a synchronous alternator?

Because if speed was used, the power system frequency would be changed. A synchronous generator spins at synchronous speeds.

Synchronous generators 101: A typical synchronous generator will have a field winding (typically on the rotor, or rotating part) and a stator winding (the stationary part where power is supplied to the power grid). Current is injected into the field winding, turning it into an electromagnet. This field current is controlled by the Automatic Voltage Regulator (AVR). The more current supplied to the field winding, the stronger the electromagnet becomes, and the more power is required from the prime mover (whatever is supplying the power - steam turbine, for example) to keep the generator spinning at synchronous speeds.