Private firms, including Verizon, will not recognize direct economic benefit from a city-wide wi-fi network. If the city were to provide such a network, the supply of a lower cost alternative for cellular data, home or workplace internet access, and/or hotspot access would be in excess. This would shift the demand for these services down, reducing the revenue Verizon currently realizes.
For Verizon, or like firms, to benefit from city-wide wi-fi, they would need to build out the system without the desire to initially (or maybe ever) produce revenue directly from providing internet connections. I would suggest a model such as Google Fiber is following. To provide a fast and overly hyped product that will create enough of a buzz to increase revenues in complementing services or products. In addition, Google Fiber access is limited to those whose needs do not require a server. This limits access to personal or small private users.
The issue for Verizon is that they do not have the suite of complementing products, such as Google does. Therefore, in the presented case, they have little upside to supporting the project.
For the City of Philadelphia, direct economic costs are not the motivation for implementing such a system. Increasing the supply of free wi-fi shifts the demand curve positively, creating a new demand curve representing the societal impact that free, city-wide wi-fi will provide. Society will realize a benefit that will not be realized by Verizon.
Philadelphia will realize many benefits including attracting business, tourists, and potentially residents because of the ease of connectivity.