I think permitting individual posts to be shared with individual users would be great! However, I also think there are improvements to be made here that aren't nearly as complex. For instance, simply being able to allow/deny reposts on a post-by-post basis, make individual posts private (as in, followers only and not displayed to not-logged-in users) and so forth is very important.
Came here to request something like this! Livejournal friends-locking is another implementation of this concept, where "following"/"followers" is distinct from "friends", but otherwise it behaves similarly to the access lists OP described. Twitter circles is another, which behaves like a single access list.
Other things to consider would be options like "unlisted" (opt out of tag searching and other discoverability options) as well as "global" i.e. opting in to this other feature request.
I think this also has the possibility of providing some of the relief being asked for in the feature request for locking replies. Can't have goons replying with weird stuff if you don't publish to the whole site.
Also for consideration: the commenters in the requests for sending people posts and @-mentions to cause a notification have expressed concerns that it could lead to spam. Making it possible to only send people posts if the post is at a lower visibility level, or only cause a notification when they're @-mentioned if they're part of the group of people who are in the lower visibility level (e.g. mutual followers), would help address those spam concerns, I think.
Honestly just want an option to "restrict a post's visibility to myself-only". I mean, Tumblr has the option. A separate page without any followers is a clunky workaround. I also don't want my Drafts to back up with things that aren't actually drafts.
The other options would be OK if they could figure out how to implement them.