Voice coil

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To get the desired impedance the number of windings would have to go up. This increases Mms (moving mass) and Le (inductance of the coil). This is not always wanted.
You also need a wider magnetic gap to fit the bigger coil.

So, it's not just a matter of increasing the diameter of the conductor to get better powerhandling (which is not such a very important parameter in most cases anyway).
A lot more parameters change when you do that.
 
You need sufficient Voice Coil to give the desired nominal speaker impedance.
That Voice acheives it's "impedance" from a combination of resistance and inductance and mechanical capacitance.

The resistance part which is often around 70% to 80% of the nominal impedance is made up by the length and diameter and electrical resistance of the actual winding.
The number of turns and the diameter of the wire (if circular) and the material (usually copper or aluminium) must give that desired Re (the resistive component of the nominal impedance).

All of this has nothing to do with the power handling. The impedance comes first, the power handling will come later.
 
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