@mijostyn I think you are talking about hearing errors in alignment which I totally agree are easily audible versus differences in the geometry you choose to align to.
But I am curious about your statement about "twisting the cartridge in the headshell a few degrees", by which I think you mean the zenith adjustment. I have yet to find any information about how you can tell in which direction and by how much your zenith is in error. Most of us simply align the cantilever since we have no way of aligning the diamond but as @macg19 points out and JR at Wally Tools has asserted the zenith error in how the stylus is mounted to the cantilever can significantly exceed the generally small errors that occur when carefully mounting the cartridge to the tonearm.
Other than randomly twisting the cartridge back and forth and listening is there any way know in what direction and by how much the zenith error (including the error in the stylus mounted to the cantilever) is? And I mean without paying Wally Tools $500 for their cartridge analysis service.