After having watched this video, specifically
this part, this is my speculation on the process (and its complete speculation):
1. They may not have an automated operations process that goes through apps to check that all the supporting docs are, instead they go app by app, by hand, checking that everything they need is there. Hence why we are getting "Your application is complete" emails at odd, non-uniform times.
2. Once an app is deemed complete, the email mentions that it moves to review. Watching the video, it looks like that review can take a while.
3. [Pure speculation] What I suspect is that the app allocation between the first readers and committee readers is randomized twice. Some lucky few might have their apps read relatively early by both readers, they both agree for interview, and the applicant gets notified fairly quickly. Others may not be so lucky, and have an app read the first time at the start of the process, and then much much later - but until they get alignment, their app won't progress.
Just my thoughts