> It reads nonzero when you are standing on Earth because of electromagnetic repulsion between your atoms and the atoms in the floor.
It works because there's an external force pushing on the surface of the phone, and not equally on all its parts, which is the scenario we are discussing.
> Because the acceleration sets up internal forces in the object that result in a different equilibrium from the one it was in while it was freely falling.
And the cause of this is what you fail to explain.
> It works because there's an external force pushing on the surface of the phone
Which then gets transmitted by the surface of the phone to the rest of the phone.
> not equally on all its parts
Yes, equally on all its parts, once you take into account that the parts of the phone can exert forces on each other.
> the cause of this is what you fail to explain
Cause of what? The internal forces? That's obvious: the distances between adjacent atoms change, and the electromagnetic forces between adjacent atoms are distance dependent. In other words, as I have already pointed out, the size and shape of the object changes when it is accelerated (in the sense of proper acceleration), compared to when it is not. Or, to put it another way, the equilibrium state of the object is different when it is accelerated than when it is not, with different inter-atomic distances and therefore different internal forces (as in, nonzero internal forces when accelerated, compared to zero when not).
> Which then gets transmitted by the surface of the phone to the rest of the phone.
But this is a very different situation than when you have an external force acting equally on all the atoms equally, and you will, as you correctly point out, have forces between the atoms. Of course in this case it is trivial, because you can easily measure the tension between different parts (for example).
But that is not the situation we are discussing. The situation we are discussing is when were are an external force on all parts equally. So there will be no tension that you can measure.
> this is a very different situation than when you have an external force acting equally on all the atoms
Gravity is not an "external force" in GR. In GR, an object moving solely under gravity, i.e., in free fall, feels no force (no internal stresses, zero reading on an accelerometer) because there is no force--not because there is "an external force acting equally on all the atoms".
If you want to say that the Newtonian interpretation, where gravity is "an external force acting equally on all the atoms", is indistinguishable experimentally from the GR interpretation, where gravity isn't a force at all, I suppose that's true. But then the "external force acting equally on all the atoms" is just like Carl Sagan's undetectable dragon in his garage. We have a model that works just as well without it, so it gets scraped right off by Occam's Razor. That is the GR position.
Also, no matter how you want to resolve the above issue, it still remains true that non-gravitational forces do not obey the equivalence principle, so there is no "spacetime geometry" interpretation for them that works. And those are also the cases where you do have internal stresses in the objects and an accelerometer reads nonzero. So again GR's interpretation--that these cases are forces while gravity is not, and that explains the difference in accelerometer readings--is simpler than the Newtonian one, where you have to argue that gravity is a "force" but doesn't work like other "forces" work.
Put more briefly, gravity does not produce a compressive stress in the phone in free fall. The external force from the table applied to the phone sitting atop it does create compressive stress. Ergo, the situations are fundamentally different.
I think the burden of explanation is on the great great grandparent post which proposed an accelerometer "entirely made out of the same magnetic field" which would let it satisfy an equivalence principle for "magnetic force".
It works because there's an external force pushing on the surface of the phone, and not equally on all its parts, which is the scenario we are discussing.
> Because the acceleration sets up internal forces in the object that result in a different equilibrium from the one it was in while it was freely falling.
And the cause of this is what you fail to explain.