FWIW, I tend to follow suite and typically update my iPhones from my computer, because I like the fact that it performs a backup before updating. That way, if the update goes wrong, I at least, have a means to restore my phone.
So far, I have not experienced any issues doing so with this latest RSR. I have to admit it happened so quickly that I didn't even know it completed until I checked the phone's iOS version which now has a "(c)" designation added to it.
If yours doesn't, I suggest that you perform a "Force Restart," and then, try updating it again while it is connected to your Mac.
Ref: Force restart iPhone - Apple Support