Recently I was building a roof with an old, very experienced builder. Turns out that on construction sites, nails and planks are always discussed in inches, even when they're actually metric. So a 60mm nail would be "a two point fiver" ("kakspuokki" or such in Finnish).
Note the inconsistency in 1/4".
What's the purpose of having mm^2? You can't measure it any easier (how the heck are you gonna measure area without calipers? you're gonna need a gauge with holes in it to identify wires), nor is it easier to express the number easily.
For manufacturing purposes, expressing the radius or diameter might be good, but for using them, the AWG number is really nice and streamlined.
This doesn't really preclude a logarithmic scale, but it should be the kind that's easy to convert (i.e. increasing numbers denote increasing area). Looking at AWG, it could actually even be decimal, like dB. Consider: 17 gauge is almost exactly 1 mm^2 in area, so if we pick exactly mm^2 as 1 on our hypothetical scale, then 10 would be 10mm - close to 7 gauge, and -10 would be 0.1mm - close to 27 gauge. And there are plenty of industries that already know how to work with dB scale, and use the shortcuts that it offers.
By the way, while looking up related things, I've discovered the existence of a weird unit called "circular mil" (basically, cross-section of a wire 1 mil in diameter) that is, apparently, already used in US for wires that are out of bounds on AWG gauge scale. Which seems to indicate that cross-section area is, indeed, the preferred metric.
There's nothing more natural about an inch than a centimeter, and nice, round, easy-to-remember numbers can be had on both scales for "natural", commonly found distances. Ditto for pounds and kilograms, Celsius and Fahrenheit, acre and hectare etc.
Objectively, metric wins because it uses the same decimal scale as our number system, and because the units are designed to establish the most straightforward relations between different quantities.
Yes, using 12 for a base has some advantages due to more divisors, but not being consistent with decimal wipes them all out (and traditional units don't consistently use 12, either - consider units of volume, for example). In an ideal world, we'd have 6 fingers on each hand, and use base-12 everywhere; alas...