I don't think that wireless connectivity is a public good, at least not a pure public good. A public good is something that is nonexcludable (I can't prevent you from consuming it) and nonrival (your consumption does not reduce my consumption). Wireless connectivity is nonrival up to a point, but it is congestible. Furthermore, we know that we can password protect and/or charge for access, which means that it is excludable. Thus on a purely technical level, wireless connectivity is not a public good.
I don't want to argue definitions with an economist. But note that the fact that wireless networks *can* be password-protected -- so that network operators *can* charge for access -- doesn't mean that they *should* be password-protected. If you assume that we're talking about open wireless, then a network for Market Square comes closer to being a "pure" public good, and we're back to my earlier diagnosis -- this may be a case for government provisioning. Put differently, if we assume the need for password-protection (i.e., excludability) we instantly identify some class of wireless users who are excluded from the network -- not by technology alone, but by price. Some substantial portion of the consumer surplus available via installation of the network would be transferred from consumers themselves to the local businesses that finance and charge for it; there would, also, be some deadweight loss.
If, in the abstract, we're willing to live with that, then fine. After all, private companies develop and charge for all kinds of things that are, like wireless connectivity, forms of "infrastructure." Electricity and other utilities; cable TV; water service; roads. But public regulation -- of price and quality of service -- is rarely far behind, because these sorts of things tend to be natural monopolies (yes, I know I'm again invoking an economist's term of art), and the risk of monopoly pricing is considerable. So if Pittsburgh somehow manages to get a private wireless network off the ground in Market Square or elsewhere in Downtown, and if the economics of that network are such that only one network is supportable, then it is likely fair -- to the citizens who would use the network -- to regulate it in the public interest.