Why would a software update fix it? Note that it doesn't have hardware support for the 5 GHz band, much like the iPhone 4.

I can't connect to any Wi-Fi networks at all. This was an issue introduced by iOS 7. If a software update can break it, a software update can fix it. From what I understand the strain on the CPU from the additional processing required to run iOS 7 causes heat to become an issue for the Wi-Fi chipset.