In a single-sideband transmitter, what is the purpose of the speech amplifier?

The speech amplifier is the very first active stage in the audio chain of a typical radio transmitter. Its sole purpose is to take the extremely weak audio voltage generated by the microphone and amplify it to a usable level. Once amplified, this baseband audio signal is strong enough to drive the balanced modulator, where it will eventually be combined with an RF carrier. The speech amplifier operates purely on audio frequencies. It does not amplify the carrier, sidebands, or RF harmonics. Those components do not exist at this stage of the radio; they are created further down the signal path after the audio has been modulated.