As Joe stated above, this isn't just isolated to their company. This was an incredibly useful feature which helped maintain emails and processes, especially with regards to shared email boxes.
The categories option is not suitable when you are having to generate multiple numbers a day to assign to these emails. It would completely overwhelm that as an option making it unusable for anything else that you have categories for already.
For example project numbers or room bookings may not be generated until after the email has already been sent, so putting it into the body of the email isn't viable at all. Unless I reply to an email back to myself with it, then continue to do that while the whole process this is updated, which is just messy and that's how emails get mixed up, and important information in the email gets pushed down to the bottom.
With regards to the "Flagging" option can you elaborate on how I can add more information on a flagged email, and if it's unflagged say moved to completed/ticked, does that information disappear?