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Without Re the circuit bias point will not be stable, since it will then depend upon the transistor Vbe, which varies with temperature.
That's why you need Re, to stabilize the bias current.
If you don't want Re to lower the AC gain then you can bypass Re to ground with a large capacitor.
It is called RE, not Re.
RE adds negative feedback to cancel most of the difference in the Vbe of transistors (the Vbe of one transistor might be 0.6V and another transistor might be 0.7V) and its changes caused by temperature. The negative feedback also reduces distortion a lot.
If the transistor will be used as an on and off switch then the two base resistors are not needed (only one in series is needed) and the emitter resistor is not needed.
Here is a simulation of the difference in voltage gain and distortion when the emitter resistor is there or is bypassed with a capacitor (then the emitter is AC grounded). The transistor is not clipping.
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