Son of a gun, I went and researched and turns out my Mac can produce a "similar" spatialization effect in VLC from 5.1 audio at least, under Window > Audio Effects > Filter > Headphone virtualization. Not that I've ever heard anyone mention its existence before. But I'm definitely using that from now on. Thanks for setting me on that track!

As for comparing the two... the iOS one is absolutely better, but the VLC one is still a really nice improvement. But it's definitely not just the head tracking. The VLC one somehow feels like it spreads the audio out "horizontally", so background sound comes from outside the head, but people speaking still sound "between my ears". Whereas with iOS, the people speaking genuinely sound like they're in front of me -- it puts the center audio forwards -- and nothing sounds "between my ears".

I would guess Apple can produce something superior because they know the exact shape and positioning of their own headphones, as opposed to a generic stereo headphone plugin?

Not to mention, of course, the lack of head tracking in VLC. I just researched Dolby Atmos for Headphones to compare, and it looks intriguing but appears to be Windows only.