The true value of this mentality isn't possible while in the current structure of our capitalistic systems.
Historically speaking, there is some degree of success to be had in convincing others to adopt this position, though, so that others can exploit them. Capitalism is at least being honest, unlike the systems that lie to you about how you can adopt this strategy. I often think that a great deal of what people don't like about capitalism is precisely that it is generally being honest and not telling you glittering, appealing lies.
Much of the criticism (but not all!) of capitalism boils down to people shooting the messenger. It is a rough world out there and you do need to find some way to compete, but some people would rather hear from people singing about how if you just give them all the power, their philosophy will erase that from the world and you can just go to sleep peacefully and stop worrying. Unfortunately, this is also a lie, or at least that's what the history shows.
Nor does this mean that we are somehow obligated to "maximize" brutality or something stupid. It means that by facing it squarely, we are better able to deal with it, and that's why the capitalistic countries of the world are far better places to be than the places that reject it. It may not be perfect, but by aligning oneself with the true nature of the world you end up producing enough excess wealth to be able to seriously engage in social programs. It's OK to wish it weren't this way... it's not so OK to think that if we just close our eyes and wish hard enough we can make the problem unexist. That leads to actions that leave you vulnerable and exposed. Facing the truth is part of the path to changing it; denial often just makes it far worse.
EDIT: It is a rough world out there and you do need to find some way to compete
That survival depends on competition is a religious tenet, an ideological rationalization.
It is a wonderful thing that humans cooperate enough that we can build enough wealth that some of us, even many of us, can forget this... but the fact that the human strategy is ultimately one of great cooperation doesn't change the fact that the human cooperation lives on a substrate of vicious, no-holds-barred competition, induced by the physics of how this universe works.
Realizing the world is built on competition is not what breeds viciousness... it is what lets us successfully build the secondary layer on top that shields us from it. Those philosophies that try to take a shortcut and declare that the world is not a competitive place have the paradoxical effect of exposing us all the more directly to the raw competition again, because it causes people to build structures that, in their denial of the nature of reality, therefore fail to insulate us against it.
The first step to solving a problem is ever and always clearly identify the problem, not refuse to see the problem.
Long story short, if you're talking about a secondary layer over anarchic brutality, I'm talking about tertiary-and-beyond ones. Obviously this is no natural law, much less than your secondary layer. And I never said that competition breeds viciousness, but if you want to argue that point, I'll take the position that your secondary layer has not eliminated it.
The first step to figuring out if you've identified a problem properly is to figure out whether you are soaking in it.
I'm actually the first to say that A: it's all energy and atoms in the end and B: the universe is awash with both and it's mostly our own stubborness that prevents us from claiming both since we don't "like" nuclear. However, even a Kardeshev Type III civilization will have to contend with the fact that its resources are finite, and as rapidly as its ability to exploit them grows, its desires are likely to grow even faster.
It's not capitalism that causes that, either... a great deal of our desires expanding faster than our resources predates the entire concept, and the problem will likely outlast it as well.
There is nothing wrong with desire, in fact desire is good. There is problem with non-sustainable practices that damage the environment which includes people.
What you're stating as an issue comes down to management, resource management and people management. Capitalism has played a role in allowing us to see what is possible when we allow people to pool large amounts of resources, when people's efforts can be directed towards a specific goal - incentivized by the organization's leadership to aim for profits. Money is a concept which is important to remember when we're talking in theoretical terms. Money is time, time is money. What can we do with unlimited money?
If that was true we would have thousands of ISPs, Office suites, etc. With way better technology and what not.
But they are all looking for ways to lock out their competition instead of making a better product. So I'm not sure the competition is what pushes us towards.