For millions of us, Google is the backbone of our digital lives. So it’s a little incongruous that to get to its many services, we generally go through carriers such as Comcast, Verizon or AT&T. In a few towns across America, Google has eliminated the middleman and started providing broadband service. Now it’s taking on wireless with Project Fi.

An affordable alternative to many mainstream and discount carriers, Project Fi routes calls and data through Wi-Fi whenever possible (hence the name). It roams on T-Mobile and...