I think you are correct in that success results in the automation of labour and increasing the capital share of economic output to functionally 100%.
I do not think it follows that this grants investors in these AI labs part of the lightcone. If they are locked in perfect competition, there is no surplus to return to investors. Investors in natural resources, land, or perhaps data collection companies could expect everything they own to become vastly more valuable. But the investors in AI labs see their investment locked in a situation where profit margins are zero, and fail to claim the portion of the lightcone that capital might have otherwise offered them.
This seems very difficult to predict to me. Whether assets recorded on paper or digitally retain any meaning post-TAI depends on how well information can be shared, whether the courts continue to function as they did before TAI’s development, and whether power centralises enough for widespread theft to be sustained.
My intuition is that the value of such assets will spike as AI capabilities increase pre-AGI. The labour impacts will push more people afraid of being made unemployed to invest in capital driving up asset prices. Accelerated R&D from AI will presumably result in the discovery of more economically efficient uses of existing resources, driving up the prices of land, minerals, electricity etc. up even more.
Whether capital retains value post-AGI seems to come down to whether you can track your ownership effectively. I’ve written arguing that reality-collapse leads to an effective end to property rights here—https://www.lesswrong.com/posts/nFrNEMFi2EwodEXXz/keeping-capital-is-the-challenge. In summary, if digital artefacts become trivial to forge, you may not be able to trace the theft of your assets or seek retribution meaningfully. Capital retains value, but you do not retain your capital.