One dictionary definition of academia is "the environment or community concerned with the pursuit of research, education, and scholarship." By this definition MIRI is already part of academia. It's just a separate academic island with tenuous links to the broader academic mainland.

MIRI is a research organization. If you maintain that it is outside of academia then you have to explain what exactly makes it different, and why it should be immune to the pressures of publishing.

If you measure organizations on the basis of how many publications they make, you're going to get a lot of low-quality publications

Low-quality publications don't get accepted and published. I know of no universities that would rather have a lot of third-rate publications than a small number of Nature publications. I'll agree with you that things like impact factor aren't good metrics but that's somewhat missing the point here.