No I don't work for Apple. I just happened to do some digging to find something that might help me take a shot at diagnosing and providing a fix and it worked for me. Note I mentioned this may work for SOME, not ALL folks.
Note also that I did not mention overheating problems.
Some of these problems with the latest update may have slightly different presentations and thus may need completely different approaches to amend.
But in my case, my object was to attempt to diagnose the problem as if it were a desktop. Using BatteryLife allowed me to look at rates of change in charge over time. Looking at all the apps that were being called into memory and eating up RAM even though I never called those apps hinted to me that this was definitely related to the iOS upgrade.
Once I actually conducted the factory reset to the original 6.1 build, and I restored my data on the phone from backup, it has behaved normally ever since.
So I posted what I found. Although what I proposed may not work in all cases, I can also imagine where the process may have failed for some folks and they didn't see a result. What I've seen with 2 colleagues of mine whose phones had the same symptoms was that they had actually placed the phone in to recovery mode, not DFU mode.
There's a big difference here, and they can be engaged via a very similar shutdown process (which I think was a really dumb idea by Apple). All it takes is mistiming your button holds. That's why I said doing this may take several runs. It took me 3 tries to get it right.
The factory reset technically should force your phone to operate as you received it out of the box, before any other apps/modifications had been implemented. If there is still an issue, then battery or some other hardware could indeed be something else to consider.
Anyway, that's why I posted, and the solution worked. So I'm unclear why you're painting such large brushstrokes to say this method will not work. These sorts of incidents can be hit or miss on both the emergence of the problem and 1 or more approaches to solving it.