For as long as public Wi-Fi has been an issue, some have argued that public Wi-Fi would compete with 3G mobile broadband. These days, that same argument might be made about Wi-Fi cannibalizing fourth generation networks as well.
"With most of the public WiFi hotspots in the U.K. being offered by fixed operators, there is a potential value shift from mobile to fixed networks," says Telco 2.0. "As the hotspots grow and critically, once they become interconnected, there is an increasing risk to mobile operators in terms of the value of investment in expensive ‘4G’ and LTE spectrum."
It's just a guess at the moment, but I suspect the concern about cannibalization will be no more correct for 4G than it has proven to be for 3G. Wi-Fi used to be a radio tail to a fixed line network. These days, it might also be a radio tail to a radio network (mobile hotspot). There will continue to be application scenarios for fixed access, fixed access using a radio tail circuit, fully mobile broadband and untethered but not mobile access.
People will use "all of the above." In some markets, where a smartphone purchase also requires a minimal data plan, that will be even more true.