why there is not a constant ratio of the insulation area to the total
area in all AWG conductors?
Because the important factor is the breakdown voltage of the insulation, and this is a function of thickness, not cross-sectional area.
The second question is: can we take the advantage of the surface
increase due to the insulation in thinner conductors and to design for
more current capacity than thicker conductors?
No, because the typical application has the wire wound tightly against its neighbors. The ability of the overall winding to get rid of heat is a function of its exterior surface area, not the surface area of the individual wires.
First of all, don't tamper with AC. Just making sure. My answer is talking about the DC side, which in this case is 12v and classified as "LVDC", a low enough voltage that is safe to work with.
On to your question, yes, this idea will work. At least when using multiple-pin connectors, this is called "current sharing". You can think of each wire being a resistor, with (in this example) one resistor being replaced by 4 in parallel. There will not be a problem, as long as the resistors are more or less equal.
This can become a problem (usually in larger loads, or with extremely small conductors) if your resistance in one of the four resistors starts going up (for example, is completely disconnected, heats up or is broken.). In a vicious cycle commonly called "thermal runaway", you can end up having more current on the individual wires than they can safely handle, thus heating them up, and having their resistance go up, or even melt themselves.
-Source: EE student and designer, have done this myself on multiple occasions, also fried many LED's due to unstable current sharing.
Best Answer
The AWG only tells you the total cross-sectional area of all the strands (or that of a single strand). The conductor diameter can vary slightly with the number of strands.
The number of strands and the insulation thickness is not part of the AWG designation.
For example, this catalog sheet shows 4 different possibilities for stranded AWG 20 wire (solid is not included):
10/30, 19/32, 26/34, and 41/36.
The finest stranding is 41/36 which is 41 strands of AWG36 wire. Because the strand diameters are rounded to even AWG numbers (and, of course, must be integer number of strands) there are slight differences in the cross-sectional area from the ideal.