I've eaten them this way too, it's quite good.
Interesting, I tend to eat until I see the seeds, it is sort of when the texture feels different from the other parts of the apple because I feel like I am kind of biting on empty space.
I might try this sometime by cutting the thing in half and eating it all (except for the stem) and see how it goes.
Right when I wanted to try this, I have no apples at home.
I did this! The core was actually fine. I wouldn't suggest eating the seeds, though. Apparently it contains something that breaks down to trace elements of cyanide. You're not really supposed to eat the seeds.
Free me from Zoobilee Zoo...