I dunno, for most people in corp environment it is a total nightmare mish-mash of to-do list, calendar, notes, and assorted hate mail from their bosses.
In short, email is fucking awful and the bane of my existence. At one point I was getting north of 200 emails a day from people demanding meetings, todos, updates, and pieces of information. Please someone... reinvent it!
Email is not the bane of your existence, people using a communication platform to do things other than communicate is the bane of your existence. Your problem could be solved quite easily with changes to policy (which is just as likely to happen as your company moving away from email).
Nobody gets 200 emails per day all directly asking for something. If you do, as already said, that's a process and staffing issue, not email's fault.
The good thing about the old subject line of an email is that you usually can tell whether it's something you need to look at now or save for later, move to another folder, or delete. You can also quickly see whether you are the main target or just CC'd.
Speed reading can also assist in processing email. Sometimes you just know whether you need to read something thoroughly, or can glance over.
AS an FYI -- I was working on the largest merger between two US banks. 150-200 emails a day was a standard for many people making it almost impossible to digest all the information.
Speed reading, as you suggest, would not be a good solution to finding mission-critical information. As far as I know, no collaboration tool exists that could handle the complexity that we were dealing with. We tried quite a few, and pushed SharePoint to its limit.