While planning is ongoing and details are in flux, discussions have centered on having the firms voluntarily cede the shares to the government, the people said. The returns on the investment could then be directed to public purposes, one of the people said, such as distributing a dividend payment to all American households.
I don't believe either of these two assertions has any chance of happening.
But such an arrangement could also pose novel governance challenges, given the complications of the U.S. trying to effectively regulate something it partially owns, while also arguably increasing the incentives for a federal bailout.
Even if by some miracle the US has "shares" of the companies not paid for by tax dollars, it creates an anti-regulation incentive, forcing the public's interest to align with the AI companies', which is going to be worth at least whatever we would have paid to those AI companies.