OK, in the meantime I have another "data point" in this mystery.
I, too, made the mistake of allowing Software Update to update iTunes to 11.4 and received the "system extension cannot be used" error message. On the first page of this thread tingly made the suggestion to delete the .kext, download iTunes from the Apple site and install it. I did that before realizing that there were four more pages to come, i.e., that this might not be the generally accepted solution; for me, however, it seems to work.
The error message did not appear during installation. iTunes 11.4 started without a problem and both my iPhone 4S and my 2nd generation iPad appeared under Devices, both being connected by Wi-Fi. I plugged each of them into my MacBook Pro using a USB cable and synchronized each with iTunes without any problem. I checked both devices. New photos appeared on each, so the sync apparently worked. I did have a problem trying to make a backup to my computer after the sync, which I wanted because the automatic backup is being made to iCloud and I wanted a fuller backup. iTunes reported that it could not start the sync on the device, despite the fact that it was still displayed under Devices. I was able to "solve" this problem by ejecting the device, powering it off, then back on, then reconnecting it via USB cable. After ejecting both devices, then connecting them to power sources, they did not automatically appear under Devices, even though they were connected to Wi-Fi. I'm not sure whether that is expected behavior; however, when I restarted iTunes they both appeared. It seems that tingly's suggestion worked for me.
I am running OS X 10.7.5 and iOS 7.1.2.
Richard