The servers have everything to do with it. There is nothing wrong with the iOS. Earlier today my iPhone wouldn't back up to iCloud. Tonight it did. I got in during a lull. Everyone just needs to relax. There may be some devices with unique issues, but by and large this is just a case of everyone trying to access the same place via the same road.
The fact that everyone has their own 5GB (or more) of iCloud storage reserved for them is irrelevant. You all still have to access it via the same servers that are being pounded by people trying to update to iOS 9, restore because of issues, upload and download to and from iCloud Photo Library, iCloud Music Library, iCloud Drive.
Until thing settle down, you won't know if you have a unique issue or if you are just suffering from the same bottleneck that most of us are. So, there is just no advantage to trying to reset, restore, erase, modify, or otherwise mess with you devices right now.
BTW - My iPhone also said Last Backup = Never, Last Backup = 0GB. Now it is all reset and normal looking because my phone was able to back up. I did not initiate it. I just plugged the phone in and let it alone for a couple of hours.
Best of luck,
GB