So why do we measure only states of |dead> or |alive>? I don't know; maybe it's evolutionarily advantageous (those simultaneously dead and alive beings sound quite bothersome). Regardless, it's irrelevant -- evidently we are only capable of making measurements in the basis {|dead>, |alive>}, so naturally that's all we'll ever see. Of course, that restriction by itself doesn't make the |dead> + |alive> state less real, only unobservable when you're coupled with the system.
Here is where the problem arises practically: The cat has an enormous number of particles, and (naturally) exists as a vector in an exponentially large number of dimensions. Observing whether it is alive or dead is a measurement along an axis that you get the equipment for by default. On the other hand, building a machine that can take arbitrary measurements of millions and millions of particles would naturally give it so much freedom within that giant space of possible axes that the smallest misalignment would take you away from the glorph basis.
The questions is why position is the preferred basis that ‘you get the equipment for by default’ - if that’s what you mean.
This takes us back to my original point, which is that although the consequences of space seem mysterious in a perspective so abstract that there is no space, they no longer seem so mysterious when you include other facts about physics, like about particles and fields. I am aware that there are some attempts underway to figure out how space could come about as a consequence of quantum stuff, but even they add extra behavior on top of the postulates of QM in order to plant the seed, so to speak, that spacetime grows from.