In all honesty, a battery is a wear and tear item. At some point it simply cannot provide enough power - it has been this way ever since rechargeable batteries was invented.
What Apple did was the only thing they could do to keep the phone working reasonably, but they should have communicated it clearly, and offered battery replacement for a reasonable price (30$ for iPhone 6 battery replacement was cheap).
Other manufactures have this issue too, and some phones like the Nexus 6p was extreme. In the old days the battery was user replaceable, and it was well known that you'd have to buy a new one at some point.
No. I don't buy this. The correct action would have been to overprovision the battery such that it is capable of advertised performance for the expected lifetime of the product instead of making the product 1 mm thinner.
Weight is important for a handheld device. 1mm thicker would add a significant chunk of weight.
The issue wasn't as much capacity, as it was peak power draw. While somewhat related to capacity, 10-20% larger battery would not have made much of a difference. They could have crippled the performance and lowering the peak power draw, but that was what they did when it was necessary.
Spikes in Google searches and personal anecdotes are not proof an issue. What has been shown was that Apple throttled iPhones with dying batteries (which they communicated they would do in the update notes for iOS 10, albeit in a really poor way). There's really nothing else to this unless someone has found another thing to this effect.
This is a mischaracterization of the issue. They communicated battery throttling poorly; they weren't "caught slowing down" iPhones.