The list of badges is currently standard across all sites. You can't earn bounty-related badges on a per-site meta either, yet the badges appear there, too (example). And some badges, like Beta, Precognitive, Sheriff, and Constable, appear on meta but can only be awarded on main. But it appears that Convention has been special-cased to not appear on meta sites (where it can't be earned). So yeah, unavailable badges are a little weird and inconsistent.
My earlier draft of this answer explained why special-casing this one badge would be messy, but IlmariKaronen pointed out a reasonable solution in the comments (and declined to write an answer): If a badge can no longer be awarded on a site, and nobody has it, then exclude it from the list.
This way there is a rule in the code, not a bunch of per-site customizations. If anybody has the badge, keep it on the list -- it says "retired", after all, and that way people won't wonder why their badges aren't there. But if it's a "closed" badge and nobody already has it, there's no benefit to including it on the list. This solution would address all badges for which this is true, not just Analytical.