Wyoming is an outlier. There are no truly big cities in Wyoming. Wilmington, Delaware is part of the Philly metro area and has commuter rail access to it, along with also being very close to Washington DC and part of the eastern seaboard megalopolis! Nevada on the other hand, doesn't have mere proximity, it has Las Vegas, which was different from other big cities for a while but has grown a lot recently in terms of population and powerful institutions.
It’s not about moving your HQ to Delaware or Wyoming. It’s about adopting the corporate law of the state of incorporation. When a company incorporates in a state like Delaware, they usually have minimal physical presence (eg. a PO Box / mail forwarding service, a firm that supplies a minimal skeleton board and does minimal corporate rituals).
I think the reason Delaware has been offering its way of doing things for so long may be the exact same reason it's being called into question now. People who had small-town ideals but called the eastern seaboard home might have moved to or stayed in Delaware because they saw it as a place where they could embrace its small-town ideals, but now it's increasingly connected to nearby places like Philly, Washington, DC, and NYC.