Why are axle cone nuts on the left side of a bike not reverse threaded? I recently discovered that the adjustable sealed bearing cartridges on my rear hub failed prematurely because one of the "cones" (cartridge shoulder nuts) had somehow tightened itself, putting undue pressure on the bearings. While I was warned that play will develop in hubs with adjustable cartridges as the bearings wear over time, I was not prepared for the opposite problem and thus did not realize what was happening until it was too late.

Because the left-side cone nut did not seem flush against the spacers and locknut when I took the wheel out, my hypothesis is that precession forces turned the cone nut clockwise as the hub turned counter-clockwise. This would have slowly moved the cone nut inward, away from the spacers/locknut. Searching "precession cone nuts" revealed a relevant thread, but I did not feel the conversation explored this topic fully.

While there may be flaws in my hypothesis, it does seem like cone nut threading would, as on bottom brackets and pedals, be an important consideration in hub design. Furthermore, while I am aware that axle locknuts should be tightened to prevent cone nuts from loosening, both nuts use a standard right-hand thread. I cannot, therefore, imagine locknuts do a very good job of keeping cone nuts from moving inward.

This brings me to my question. Why are axle cone nuts on the left side of a bike not reverse threaded? If this were the case, it would seem that precession forces would effectively keep cone nuts on both sides of the bike flush against their respective spacers and locknuts.
Cone nuts have lock nuts.  The lock nuts (in an ideal world) prevent any motion.

And, as you observe, precession in either direction is bad on wheel bearings, so there's no real point in preferring self-tightening or self-loosening.

(In fact, having both the same direction means that any slight "creep" in one will tend to be canceled by the "creep" in the other.)

Note that crank bearings and pedal threads are subjected to much more axial load (and more intermittent), and are thus more subject to creep.  Plus, cartridge crank bearing cups and pedal threads are self-limiting -- they will only tighten so far, regardless.  And often the crank cups do not have lock nuts.