By design, Stack Exchange is based on community moderation. Non-moderator community members have access to almost all of the tools to do content curation/moderation. Even brand new users can identify edit needs and suggest improvements. There are relatively low rep thresholds for contributing in the review queues, and modest thresholds for performing most content-related moderation without review.
Moderators can do some tasks more efficiently than other users (e.g., single-vote mod hammer and no daily volume limits), but the moderator-specific tasks fall into a few categories -- user moderation, certain infrastructure maintenance, and certain content maintenance like comment threads and question migration.
While moderators are typically very active, high-rep users, who continue to volunteer time for content moderation, content moderation isn't generally a moderator responsibility (the moderator role is often described as intended to be an exception handler).
2021: a year in moderation provides some interesting stats. Note that it doesn't include some of the routine content curation, like editing posts outside of review queues, or providing help/guidance via comments. One thing that stands out is that much of what should be the community's responsibility has been handled predominantly by moderators.
Note that there is not a current problem with community moderation in the sense that the needed work is not getting done (although there are some proactive topics with few users interested in pursuing them). Everything that needs to get done to keep the site running smoothly and generally maintain quality is getting done, and on a timely basis. But that's happening because the posting volume is still low, and a disproportionate share of the workload is being handled by an extremely active moderator, who manages to handle a lot of stuff before other people notice it. That isn't a good long-term solution.
Long-term site success requires a greater level of community involvement. In fairness, the workload should not fall so heavily on the moderators. Beyond that, there is a need to develop the skills and experience (and sense of priority) in a broader base of current users and potential future moderators.
This question is to spur discussion on why community moderation is so minimal, and what we can do to get more people involved in it. I'll kick it off with a few thoughts in the form of answers. Readers should feel free to add answers covering other aspects and ideas, and to flesh out any of the ideas I've posted.