I *absolutely* disagree on readability. I think title case actually increases readability because it emphasizes nouns and verbs — which are the elements that convey the meaning of the message. If you quickly glance at a text, it makes it easier to scan for those elements. Yes, for longer texts it decreases readability, but for quick glances at short texts I think it increases it. And titles should be short!
I think Apple’s alert title in your example is a bit long (it’s supposed to be a title, after all!), but I like what they’ve done there: the text is not just randomly divided into three rows, but the meaning is grouped by them as well. Emphasized in the first row is [Turn On Location Services], in the second row [Allow “Weather”], and in the third row [Determine Your Location]. Do something to let the app do something to get a result. Personally, I’d have shortened it to “Turn On Location Services to Determine Your Location”, but I guess Apple wants to be clear that users can determine this on a per-app basis. The title is indeed rather long, but it also contains all necessary information. Google on the other hand? First of all, the title doesn’t contain any information at all and ends with a question mark. So yes, the title is shorter, but it necessarily requires you to read the body text as well. Also, it’s badly formatted: first row reads [Use Google’s location], second row [service?]. The keyword is “location service”, which should be one term with a non-breaking space. They could have left out “Google’s” to make it fit in one row; because nobody cares where location services come from, just what they do.
So I think neither are particularly good examples. But I do prefer Apple’s because it contains more information and it seems that at least there was some thought put into the formatting.
Also, I think it’s worth mentioning that while the English language mostly uses lowercase, other languages don’t. In German for example, nouns are always capitalized. I believe it increases readability because it introduces a hierarchy of words. Nouns tend to be the most important elements in a sentence, so they are highlighted that way. We just don’t capitalize verbs; otherwise title case and “German case” seem rather similar. So in a way there is some natural language history in title case, it’s not just based on some businessmen feeling the need to have “gravitas”.