The point isn't necessarily that stores need to spring up nearby, the point is that it needs to be easier to access stores (eg by making it easier to get transportation).
Well in my experience the rich and poor rely on public transit in mostly similar numbers, so I don't really see what transit in particular has to do with it.
Ideally you'd want businesses to voluntarily operate in these places but it's hard to get them to. It is difficult to operate at a profit in these environments. Margins are worse because poorer populations can less afford luxury items. Costs are higher due to increase in theft, the need for additional security services, and insurance.
In recent years there have been high profile closures of big brand stores in major metro areas for exactly these reasons. Proposals to address grocery store closures include regulating them in San Francisco with a lengthy 6 month notice period and other requirements. In Chicago the idea has been floated for government run grocery stores.
While the jump to call such moves "the moral equivalent of slavery" is a bit extreme, they do exist in the realm of compelled behavior and against liberty. In the case of SF it's with regard to making it more difficult to exercise the decision to close a store, which may require the operator to take financial losses for longer and incur additional compliance related costs. In the case of Chicago, it's using tax payer money (which is collected through threat of incarceration) to operate a service that's traditionally provided voluntarily by a private actor because it yields them benefit (profits).
Weird conclusion to jump to. GP did not suggest grocery stores staffed under threat of jail time anywhere.
Better public transit benefits everyone. Better urban design favoring walkable neighborhoods benefits everyone. Better zoning allowing neighborhood shops at street level benefits everyone.