Question: "What makes you think the GEM has a higher "accuracy ceiling"?
Answer: "an ALTAZ mount is just an EQ mount with really poor alignment."
Also, I've seen videos saying, "Yes you actually can do astrophotography with an alt/az!" but then they go on to say "with shorter exposure times" and this or that procedure to compensate for the tracking... which is basically admitting that while it is possible, a GEM really would be more accurate in the first place. Some of that is about field rotation and guiding accuracy and in this context those factors don't matter. I just want to be able to slew between targets and have it dead center. Since I only do a little visual, I'm not that fast at finding targets, and it's for an outreach event so I want to spend as little time hunting as possible.
But perhaps the comment "an ALTAZ mount is just an EQ mount with really poor alignment" was meant to indicate that if the software map can handle alt/az, then it can also handle an arbitrary level of misalignment in EQ mode. How the software model deals with mechanical misalignment is essentially what I am asking about, but I would not assume that it can handle arbitrary misalignment nor that the models are the same. Case in point: in EQ mode, manually slewing to Polaris is tricky - I don't mean using the adjustment screws, I mean using the motors and trying to get Polaris centered could involve meridian flips just to get the star to move a tiny bit in the field of view. The software would need to address the same challenge within its code. But in Alt/az it's a piece of cake. Also, in EQ mode I have sometimes tried doing a 3 star alignment without spending much time on mechanically aligning the axis and the alignment fails.
Theory aside, I suppose that is the experience that is driving the question. On my old mount I had to put a fair amount of time into the polar alignment or risk having the 3 star alignment fail.