The two former projects have been deemed "canon" by the creators. The latter has not. "Canon" is determined by the creators. One can accept this or notone's individual preference does not really matterbut that has no effect on the meaning of canon and how the story "officially" unfolds. If the stories were not meant to be logical continuations, they would not have been deemed "canon" from the outset.
Until there are significant contradictions between events in the canon gamesof which I don't believe there have been any so far apart from minor things like historical dates (though we'll need to experience PQ, P4AU and P4D to determine this for sure)it still has meaning.
Worth pointing out that Atlus have never used the word canon to refer to anything.
All they said is that it's a proper sequel and a continuation of the storyline (and no that isn't an exact quote, so please don't point that out.
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I don't think it's that weird. To me, it just suggests that they want to avoid thinking in those terms, which is supported by neither character having a set name in PQ either.
Personally, I think fretting about what is and isn't canon to be unnecessary to one's enjoyment, and suggest that you take away what you want, which is quite easy with the right perspective. My choices of protagonist or social links or endings or names are mine, and that's what make the games special to me, and canon can only overshadow that if I let it.
To a point, I'd agree, but I also feel like respecting canon is important, and pulling crazy things with the canon (as Persona has done) can be frustrating for fans.
Let's say I finished Persona 3, and I decided that, in my head, Akihiko became a policeman and married Mitsuru, and they lived happily ever after. Arena then comes out after this and says that actually Mitsuru became all kinds of weird and Akihiko became a wandering wild man. I can pretend otherwise, but really, I'd know it isn't true. So the only solution is to not do it.
But then, of course, you're ruling out sequels. And whilst they could keep the characters on a more similar path to Persona 3 to keep fans like me happy, there're probably some fans out there who figure that this is exactly where Mitsuru and Akihiko would go in life.
I think what I'm trying to say is that you can't please any of the people any of the time, and so nobody should make anything.