Common emitter amplifier biasing and resistor selection
Of course, you are allowed to make Rc=Re. However, the question remains if this make much sense! Hence, I think the first rule you have mentioned (Vc=Vcc*2/3 and Ve=Vcc/3) is a good trade-off between allowable swing and good stabilization of the operational point. As you probably know, the resistor Re provides negative feedback for DC and stabilizes the bias point.

Regarding your example (Vcc=12V). In this case the possible (theoretical) swing is 12-8=+4V and 4-8=-4V with Vce=4V. 

Of course, the resistor Re provides also signal feedback, thereby reducing the gain to a value of app. Rc/Re. For larger gain you can bypass the resistor Re with a suitable capacitor.