Some people say that using an iPhone-, iPad-, Watch-case does reduces the life expectation of the battery. I could imagine that it's true, because the heat drain becomes worse. On the other hand is the protection that the device gets from using a case beyond doubt.
Is it proven, that protection cases decrease the life expectation of a battery?
What's the general recommendation concerning protection cases? Does Apple self recommend it at all?
You cannot answer your first question in general as it depends on the protection case itself.
If the protection case does not transfer heat adequately and contributes to a higher temperature phone - then yes, that would ever so slightly decrease the life expectancy of the battery.
If the protection case does transfer heat adequately - or more even better than adequately, it could make no difference for the life expectancy of the battery - or it could even increase the life expectancy of the battery.
In any case, if you use a "normal" protection case (i.e. don't use one made of 30 cm thick wool or something like that) - I wouldn't worry one bit about any impact on the life expectancy of the batteries.
As Apple themselves design, manufacture and sells various covers and cases, I'm sure that Apple doesn't in general have a problem with devices being protected in that fashion.
