When you click "edit" on a meta site as a non-edit-privileged user, the error message appears:
Suggested edits are not allowed on non-tag-wiki posts on meta sites.
Right as I was going to post this as a possible bug, I finally found this post which says that per-site Metas don't have suggested edits by-design because it's "not needed".
However, I've been participating a lot over at Skeptics meta where there is a lot still to be figured out in terms of site guidelines. The Meta is one of the most active I've seen and a lot of the questions are really trying to gather community-built suggestions. So maybe more of those need to be Community Wiki, but it still brings me to ask why don't per-site-metas "need" suggested edits?
Adding bounty: The more betas I participate in, the more I don't get this.