Maybe centuries ago that was true. In the modern economy, workers are already extracting the full amount of value they generate[1]. Profit for a business comes from the additional value its capital is able to generate on top of the labour value.
[1] Within reason. The market is never perfectly efficient. Sometimes workers see slightly less – sometimes slightly more – but not anything hugely out of line.
Can you provide a concrete example of capital generating value without the involvement of any labor?
Not all the way there, but surprisingly close.
Let's face it: labor is soon to be obsolete. All economic models that include labor will become antique notions, similar to factoring in horsepower.
Gonna be a rough road: all folks in power can think of is, how to keep workers slaving away at something, anything, so long as they don't revolt.
People in the US have consumer items, pointless dictatorial jobs, and insane stress from having the welfare state stripped for parts by venture capitalists. We aren't even enjoying what we have even though materially, a good fraction of the population have more than so many others. If you lose your pointless job, you lose your home, healthcare, and transportation and are considered a surplus person.
These are all political choices.
If we fix some baseline combination of quantities of "labor" and "capital", and compare it to some later combination where both have been increased, there are a number of possible differences to take.
There are V(l_0, c_0) , V(l_0 + dl, c_0), V(l_0, c_0 + dc), V(l_0 + dl, c_0 + dc).
One could call V(l_0 + dl, c_0) - V(l_0, c_0) "the contribution from additional labor", and V(l_0, c_0 + dc) - V(l_0, c_0) "the contribution from additional capital", or one might call V(l_0 + dl, c_0 + dc) - V(L_0, c_0 + dc) "the contribution from additional labor" and V(l_0 + dl, c_0 + dc) - V(l_0 + dl, c_0) "the contribution from additional capital".
In a linear approximation, these two ways of assigning quantities to these names for quantities, could be the same. But I wouldn't really expect them to be the same in practice, at least for large values of dl and dc. (note: I am using "dl" and "dc" instead of \Delta l and \Delta c, because it is more convenient to type. I don't mean to suggest that the changes are extremely small or infinitesimal, as might be suggested by using the letter d instead of \Delta.)
As such, I think that "the additional value that an additional amount of capital is able to produce" is a meaningful value if "quantity of labor" is held constant, and that "the additional value that an additional amount of labor is about to produce" is a meaningful value if "amount of capital" is held constant.
When both values are changed, then how much to attribute the increase in value produced to, is I think inherently somewhat ambiguous, but also not a completely meaningless question.
Given the four values V(l_0, c_0) , V(l_0 + dl, c_0), V(l_0, c_0 + dc), V(l_0 + dl, c_0 + dc), assuming that all four of the differences I mentioned previously are non-negative, then clearly the additional value from either cannot reasonably be said to be more than V(l_0 + dl, c_0 + dc) - V(l_0, c_0). Nor, I think, can the value attributed to the change along one axis, be reasonably estimated as less than the minimum of the differences along that axis. Also, I think probably a more reasonable upper bound on either contribution, is the maximum of the two differences for the respective axis.
Now, maybe your goal is to talk about the deserts, rather than causes? But if we are talking about what things are causally responsible for how much of something is produced, I think it's pretty clear that this analysis in terms of differences of these 4 terms, is on the right track.
The core claim is that simply buying things and managing things produces value all on its own and it's transparently false as if the thing wasn't produced, you couldn't buy it.
The other core claim is that there's a legitimacy to the idea that if you buy something that is socially useful, you get to derive the exclusive right to the fruits of it which makes no sense.