investors don't perform work (labour); they take capital risk. An ai do not own capital, and thus cannot "take" that role.
If you're asking about the role of a manager of investment, that's not an investor - that's just a worker, which can and would be automated eventually. Robo-advisors are already quite common. The owner of capital can use AI to "think" for them in choosing what capital risk to take.
And as for massive number of people who don't have income - i dont think that will come to pass either (just as you dont think AGI will come to pass). Mostly because the speed of these automation will decline as it's not that trivial to do so - the low hanging fruits would've been picked asap, and the difficult ones left will take ages to automate.
If a bootstrapped startup has immediate access to the equivalent of 20 administrative employees via AI, then what purpose does the investor have?
And if a single bootstrapped "investor" can support such a company, that's an even better world than today isnt it? It means everyone has a chance at breaking out with a successful company/product.
Producing things cheaper sounds great, but just because its produced cheaper doesn't mean it is cheaper for people to buy.
And it doesn't matter if things are cheap if a massive number of people don't have incomes at all (or even a reasonable way to find an income - what exactly are white collar professionals supposed to do when their profession is automated away, if all the other professions are also being automated away?)
Sidenote btw, but I do think it's funny that the investor class doesn't think AI will come for their role..
To me the silver lining is that I don't think most of this comes to pass, because I don't think current approaches to AGI are good enough. But it sure shows some massive structural issues we will eventually face