Several problems with your proposition:
1. Not all capital was originally acquired by providing valuable services. The families of the still wealthy aristocrats of Europe and Latin America originally acquired their capital generally by being more successful thugs than others. I'm not sure those are valuable services to society.
Simiarly, drug lords in Mexico, oligarchs in Russia (who essentially stole the country from positions of influence in the government) and organized crime guys in the US acquire capital and often pass it on to their descendants. Their services to society are mostly if not entirely negative.
Historically speaking, crony capitalism has been much more common than free market capitalism. Those who acquire capital this way aren't providing valuable services, at least that's not the main reason for their acquisition of capital.
Indeed, historically speaking the main way to acquire a lot of capital is to invade somebody and take their stuff.
2. Second, third and twelfth generation descendants of those who originally acquired the capital by providing valuable services enjoy the benefits of that capital without in most cases providing equivalent ongoing value to society. IOW, in my opinion those who earn money in legal ways have a moral right to its enjoyment while those who inherit that money from them have only a legal right, not a moral one. Or rather their right to it is not a moral one in the same way.
Thanks for posting an interesting proposition. As you can see, I don't think it holds true in all cases, but it obviously does in many.
I don't care how you got $1000 dollars. You could burn it or eat it or hang it on your walls. If instead you lend it or invest it and earn an income by doing so, that income is rightfully yours for the useful service you have provided by not burning, eating, or hanging it on your walls, and instead lending it out or otherwise making it productive to the uses of other men.
When a socialist or a radical decides to arraign every owner of property before the bar of his private ideological requirements, and decides that no actually he isn't thoroughly Stalinist enough, or thoroughly libertarian enough, or holy enough - to me it makes not a damn bit of difference which piety is alleged, because its is a mere allegation and impudence regardless - and that therefore he doesn't deserve his property (or the income from it), and therefore it is just peachy to rob him - that is exactly what I am denying as the characteristic political evil of our time. On all sides.
Nobody needs an OK from you to own anything. If he owns it he owns it, its his, get your grubbing nose out. And if he then makes is available to productive uses, himself or by lending it out, he furthermore deserves the earnings his capital generates. And, to put it in a walnutshell, you don't.