Iphone Restore Worked for Greyed Out WIFI on 5s
There are (very) many online articles about the problem with the greyed out WIFI tab. The 4s was probably the most vulnerable to this problem and gets the most attention from users, and there are even several online services that offer to fix the 4s for a fee, but there is relatively little mention of the 5s.
My almost new 5s suddenly lost WIFI connectivity about a month after purchase. It is a replacement phone from the Apple Store that an ebay seller offered for sale when he/she opted for the new 6. I noticed a sudden runup in data usage and had the usual symptoms, and found the standard homespun solutions online, including the freezer-hairdryer strategy and the reset of network settings. The local techs I called (I live several hours from an Apple store and had no Applecare) essentially said it was a motherboard/wifi chip problem that could not be fixed reliably.
Admitting defeat, and stupidity for not finding a phone with sufficient warranty, I replaced the phone with another and went about swiping the old and preparing to transfer to the new. Lo and behold, the old 5s WIFI came to life after it was restored to factory settings, just as your article suggested. It was the one strategy I had overlooked. Freezing/heating was a waste of time, but the backup/restore procedure in iTunes brought the WIFI section of my 5s back to life.
I was then stuck with what seemed to be two fully functional relatively new iphones. I couldn't very well sell the previous one on ebay in good conscience without admitting to its problems and taking a hit financially, though it might never have the same problem again. It might also be a solder connectivity issue that may return at any time.
As things turned out I offered the phone to a friend who had been looking at finally upgrading from a 3gs (really) to a 6. He knows the story and has offered to buy the phone on installments if it continues to work. If WIFI dies again, it will be returned and I can ask a local tech who offered to re-flow the solder to the chip for a small fee.
Too long a story to share my experience that the backup/restore procedure seemed to fix the greyed out wifi toggle on an iphone 5s. Thanks!