[csense]

We developed tool use. Canines are of little use in eating fruit, but they are very useful in fighting. The Homo line developed tools to do the fighting for them, and the canines tapered off accordingly.

Although I don't agree with your conclusion here, I can certainly understand the reasoning behind it

The gradual regression of this genetic expression on the population level, to my understanding, had to be the result of either Genetic Drift, or Natural Selection.

1) Genetic Drift.
According to evolutionary biologist, Douglas Futuyma, Genetic Drift is entirely random, and in those cases where the trait is neutral to survival and reproduction, it is not subject to natural selection¹

I think you would agree that isn't the case here, not only because the trait isn't neutral to survival, but because the random nature of the genetic expression would falsify any correlation to the advent of tool use.

2) Natural Selection
This seems to be the only mechanism, along with mutation and/or recombination, that can account for the regression and dominance of the trait within a population, and lend support for a causal relationship (even if by argument) to tool use.

The problem is, since the expression of the trait itself is random, then at any given time, and at any given step of the regression, those organisms will be competing with otherwise normal, fit, organisms of the same species, at the same time, within the same population.

It follows that any morphological change that isn't neutral, which your proposition is not since it effects survival, must be equal to, or greater than, the morphological benefits of a normal, fit organism of the same species it is in competition with. Anything less than equivalence would immediately infer a disadvantage, and grounds for falsification that it would dominate a population.

In short, the adaptability of mutated organism A, must at least be equal to the adaptability of normal organism B, throughout the entire process of morphological change from generation to generation. Each new instantiation must be equal to the one preceding it, reducible of course, to it's normal fit state.

Although it's possible that the trait would dominate a population, I simply don't see any selective advantage that it would do so.

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Sources/notes
1. "You can’t have any evolutionary change whatever without mutation, and perhaps recombination, giving rise to genetic variation. But once you have genetic variation, there are basically two major possibilities: First, there is simply no difference between the different genotypes or different genes in their impact on survival or reproduction, and in that case, you can have random changes of one versus the other type in a population or a species until eventually one replaces the other. That is an evolutionary change. It happens entirely by chance, by random fluctuations. That is what we call the process of genetic drift. * Genetic drift is very different from possibility number two, natural selection..."
Interview with Douglas Futuyma

[MHalblaub]

It follows that any morphological change that isn't neutral, which your proposition is not since it effects survival, must be equal to, or greater than, the morphological benefits of a normal, fit organism of the same species it is in competition with. Anything less than equivalence would immediately infer a disadvantage, and grounds for falsification that it would dominate a population.

You rely on "the survival of the fittest" and therefore only something better can survive. But that is not true at all. Why? Very easy to explain.

A population is not located in only one place where all are always competing with each other. In fact populations are dislocated.

If the environmental pressure is lowered then more or less handicapped individuals can survive. And diversity even is needed to adapt to changing environments.

For me it's not "survival of the fittest" it's "the dead before breeding".

Human examples:
A woman died due to breast cancer with 45 years but she got 5 children. A physical healthy woman died with 89 year but without children.

Quarterback and a cheerleader died during a car accident because one of them drove drunken and the other one was an idiot driving with the drunken one. The biggest computer nerd would have driven safely.

You'll will never know on what field you'll need to fit to survive. Maybe you must run very fast maybe you have to survive a long time without meal. The advantage useful to your father must not be useful for you.

Although it's possible that the trait would dominate a population, I simply don't see any selective advantage that it would do so.

Because there is no "selective advantage" for just one trait! Your reasoning is monocausal and therefore not applicable to living matter.