They already (at least Target and Walmart) do the “cheaper online than in store”) - if you catch it they’ll price match themselves but who is checking all prices every time?
For people to vote with their wallet, there has to be an alternative. In "dead" markets where there is only one realistic alternative, whoever holds the monopoly can do whatever the fuck he wants, captive audience.
And no, it's not possible to compete as a startup against Walmart or any other of the corporate giants (and not just in retail, it's valid across industries) - alone because the sheer scale of Walmart allows them to extort insanely cheap pricing out of vendors. Walmart can sell for far cheaper than any mom and pop store can acquire.