Everyone profits from healthy competition.
That's incorrect. A competition has by definition and necessity at least one loser. The loser doesn't benefit from the competition.
I can't expect others to pay me in excess of my value.
There is no rational system of value assesment of your skills or of your work. To even think that there could be a system that rationaly sorts out the value of things as radically different as "accounting" and "washing respectfully gran-gran everyday so that she retains a modicum of human dignity in her final years" and is absurd. Value is currently imparted by people who have the most resources and, without surprise, what those people do and what those people like has the most value irrespective of any other forms
I don't see taking the wealth of others as adding to my wealth. I'm then just being carried along by the work of others. I think think anyone really wants this and would clearly avoid it if they knew how.
That's what every business owner does though. They take the work of others to make money and add to their personal wealth. Everybody does this since that's what living in society means. We all rely on other's people skills and work for our lifestyle and other people rely on your or my skill for their lifestyle and together we can make this stuff called "civilization".
Our current economical and political systems were built by aristocrats, wealthy merchants, bankers and early industrialists. Without surprise what these men did, were good at and wanted to do was judged of utmost value and thus the way to generate wealth. The closest you are in behavior, appearance, values and skills to those people the easier it is to become wealthy. The furthest away you are the least wealth you will have.
And increased the wealth of everyone in doing so.
Not really no. To amass such wealth some people get a lot less from the sweat of their brow then others. That's why Jeff has so much billions he doesn't know what to do with it while many of the people who help make Amazon such an efficient company struggle to make ends meet. Thanks to Jeff's decisions, they get next to nothing from their skills and work even if without that work the entire edifice of Amazon would collapse. Jeff increased his wealth and provided a service to customers, but he did not increase the wealth of the average "Amazon grunt". In fact, the rising level of wealth inequality shows that Amazon, Jeff and others like him and like his company have decreased the wealth and purchase power of a solid chunk of the population.