I don't think it's possible to be completely FIFO because there will be leapfrogging of applications due to the various places they can get hung up based on individual situations, such as waiting for security checks to be completed. Despite some obvious exceptions in this forum, they do appear to be moving through the queue based on some means of application date, be it AoR, DM, or some other combination. There's really not enough information to know for certain.
The online status gives us an idea of what stage the application is in. Sure, it could be more granular in showing what has or hasn't been completed, such as the information you can receive by ordering your notes. When you get a test invitation, you find out which office is handling your file.
However, given the way I've seen people in this forum react to and use that information, I certainly don't think it would be a good idea to make the online status more granular. The general public doesn't understand enough of what the process entails and IRCC aren't going to ever, ever give that information out anyways because of security implications. (Especially since one of the biggest bottlenecks is CSIS.)
I do think they would do well to allow people to pick their own oath ceremony like you can choose interview times with NEXUS.