The issue is, having to run an IMAP (or POP) server is something else that's not directly connected to our main mission, something we're not very good at (none of us have any real experience with mail protocols; although most of us have run mail servers in the past, that's totally different than generating the things that will appear through the server), and something that doesn't carry a tremendous amount of value-added. To borrow an oft-mocked term from management-speak, it's not playing to our core competencies and it's not something that improves the site as a whole for everybody (only a very few people, mostly geeks, would use this, and while we're not opposed to implementing things that make life easier for a few people, we are opposed to implementing things that only affect a few people when it takes on a lot of maintenance and upkeep in areas that we're not very experienced in).
An example here is the old "LJTalk" jabber server -- very few people used it because they all had their own messaging systems already and it fell prey to the bootstrap problem, and maintaining the server (which had to be custom-built to support the LJ integration) was something that nobody really cared about and nobody was good at. Result, something that was down more often than it was up and that made LJ look bad because it wasn't very well maintained. We don't want to get into that pattern unless there's a very compelling reason for it.
The core impetus of your suggestion seems to be "make the inbox accessible via IMAP so I can clean it out more easily", which isn't a highly compelling argument to me, mostly because we do have a bug already open to revamp the notifications system so that you can bypass inbox notification. (LJ has already done this, but it's a massive undertaking and we've diverged far enough from LJ that we can't import their patches anymore.) Absent a much stronger reason why this would be a good thing for the majority of the users (not just a few outliers), I really don't think this would be a good use of our time.
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An example here is the old "LJTalk" jabber server -- very few people used it because they all had their own messaging systems already and it fell prey to the bootstrap problem, and maintaining the server (which had to be custom-built to support the LJ integration) was something that nobody really cared about and nobody was good at. Result, something that was down more often than it was up and that made LJ look bad because it wasn't very well maintained. We don't want to get into that pattern unless there's a very compelling reason for it.
The core impetus of your suggestion seems to be "make the inbox accessible via IMAP so I can clean it out more easily", which isn't a highly compelling argument to me, mostly because we do have a bug already open to revamp the notifications system so that you can bypass inbox notification. (LJ has already done this, but it's a massive undertaking and we've diverged far enough from LJ that we can't import their patches anymore.) Absent a much stronger reason why this would be a good thing for the majority of the users (not just a few outliers), I really don't think this would be a good use of our time.