
the 5k pot is one of the parts that sets the DC conditions of the transistor, along with the base bias voltage. the 47uF cap bypasses (to ground)
some portion of the 5k, but only for AC, determined by the pot setting. the gain is set by the ratio of the collector resistance to the emitter resistance, and bypassing the pot lowers the emitter resistance
for AC signals, without changing the DC conditions.
if lugs 1&2 went to ground, the AC gain will still vary, but the DC conditions will also change, upsetting your carefully chosen collector voltage, and producing distortion on signal peaks.
search for emitter bypass cap, you'll find plenty of info.