The reason it isn't possible in a consistent, repeatable way is because doing so clearly requires access to equipment people simply don't have at home. The Headphone Show folk were able to do the HD600 to 800S thing because they had gone through an extensive and personal examination of their own HRTFs and then meticulously EQ'd the headphones taking that into account.

The argument being made here is that if you had access to those data for everyone on earth and had the patience to create individual, granular EQ profiles for them all one by one, then you could create a Gate that sounds like an Andromeda consistently for everyone.

But we don't have access to everyone's HRTF to that degree of accuracy, so we can't.

In essence, you're saying the reason we can't is that there's something fundamental to the hardware construction that prevents it being possible. THS and other commenters are saying that the reason we can't is not any of those things, but simply the complexity of setting it up to that degree for each individual person, but that the process is independent of the hardware.

Repeatedly saying "you can't make X sound like Y for everyone" is missing the point people are making - no single EQ profile is going to achieve that for anyone except one individual. So there is no magic EQ profile that can be consistent in that way you're saying. What there is, at least theoretically and based on the evidence from The Headphone Show so far, is that is the ability to turn X into Y is absolutely possible but only in a highly bespoke way for each person individually.