Perhaps you can say anecdotal, but during the holiday, of the people who were here visiting us, 5 out of 8 phones have the issue since updating to 10.1.1. The interesting part was that only 2 of us knew that any other people were having a problem. Three just thought it was their own unique experience and have been struggling with the issue for many weeks now. Super frustrating. And a sudden inability to use your phone the way you have after an upgrade certainly is a very measurable issue and hence not quite so anecdotal.
Where the problem may be is generalizing to the overall population of iPhone users. Without data there is no real way to know just how pervasive or not the issue is. Apple of course won't usually provide such data since they will likely roll out a fix under the table and then the issue will go away.
Yes perhaps a small number of the total iPhone users or perhaps not. It reminds me of a disease where some people die of the disease, some get very sick, some have a partial sickness. but nothing to slow them down much and some people seem to have nothing except you can measure viral loads in their systems. These phones are complicated entities. But how many are actually affected can vary.
You say all of the people you know on iPhone 5, 6, and 6S's are completely unaffected.
I know of at least 8 people with those models of iPhones who are affected and I live in a small community and have a fairly small acquaintance. And I keep hearing other anecdotes of dozens of other people my few friends know of who have started having problems with Shutdowns and poor battery life since the update. Perhaps the % of people lies somewhere north of the zero % you seem to know.
Anyhow.....some statements are anecdotal statements. But not all.
For those with the issue it is causing mayhem just now.
And the issue is definitively to varying degrees consequential.
"Give me 100 000 affected people, and what that means that there are 0.0025% of affected users. Means, no issue whatsoever, and industrially, an awesome engineering feat."
That is an irrational statement. 100K users whose phones cause them lots of consternation for months is not awesome in any sense. Such things can be the nidus of a snowball going down hill since much of what drives people to make purchases comes from the reputation that their device will perform. This is even more so when the device is a de facto extension of our modern sense of ourselves as people. People live and breath these devices and a failure of 100K devices would really drive social media. Not inconsequential at all as you seem to assert.
In the latest Samsung debacle they sold 1.6 million Galaxy Note 7's. A total of 85 original phones and 55 replacement phones were linked to overheating incidents in the report I read. So basically 0.00008 users were affected in dramatic fashion, but it led the recall and disabling of all phones sold. A massive problem of perception and a blight on the company Samsung which will likely linger in the psyche of the world for a time to come.
Luckily for Apple this isn't a real safety hazard, but just a PITA.
Perhaps it is the Samsung issue combined with issues such as this and those issue with the new MacBook Pro that is driving them to Start up their own Battery division. They need a Battery division in house.
Great move Apple because as we are learning, a small number of defective devices can have an almost hormonal compounding effect.
Anyhow all will likely work out well ultimately and Apple will figure it out, but while you are busy discounting the affair as generalization and anecdote, I have a phone sitting on my desk whose chief function is to be a paper weight because it no longer will hold charge for more than about 10 minutes.
The 5 works just fine while plugged in though. I just can't take it anywhere for very long without it being plugged in.