Having a finely grained street grid is incredibly important to walkable communities, as the above graphic from the Sightline Institute demonstrates. These side-by-side maps show how windy, disconnected, suburban streets make it difficult-to-impossible to get around on foot.
This is why Happy City author Charles Montgomery noted in Slate that "cul de sacs are bad for your health." It's also why advocates for healthy cities were horrified and amused when Cato Institute "scholar" Randall O'Toole recently suggested turning gridded streets in rust belt cities into cul de sacs "so that criminals have fewer escape routes.” Spending lots of money to ruin the street grid is an absolutely terrible idea, especially in cities struggling to provide basic services to their residents.
As Transport Initiatives, a U.K.-based transportation consultancy, points out, the one-mile walk coverage could be extended even more in the first example by adding some diagonal routes, like the street grids in Chicago and Washington, DC.