Yes,and some people still believe they have control of the spinning pirate's wheel in the current event, and can stop it directly on the prize they want - they SWEAR to it. Tell them it's just a tuned video animation to give you a more authentic experience, and they discount that explanation.
It's hard to convince people that underneath the viral folklore that rampantly circulates and is embraced by some guild leadership that you WILL NOT start GE until that cup turns non-gray (or else you will be summarily booted...), authentic implementation for how this is all done - and it's not smoke and mirrors. Many of us that write code for some of these exact functions really DO know what's going on and how it's done.
We don't need Inno engineering to tell us what we already know.
SO why does it take "15-30" minutes to give you personally the reality that already exists? Because it's more than just the computation math of who your competition is, it's the broadcast to you and a few hundred thousand (probably a lot more since dormant guilds with as few as 3 people have to still get competitive pairings..) people in all worlds - as well.
If they do the competitive pairing math anytime before GE opens (8 am sharp), they run the risk of a guild folding or becoming non-viable - and then they give you an empty competitive slot/stub, that in real-time, doesn't exist. At least when they pair you it did, so they will have to deal with it afterwards if it folds (and gets deleted).
It's more fun to speculate (or test??) if someone in A world gets their GE competitive assigments a few minutes after GE opens, while someone in Z world get their's later (ie, the reporting to the clients goes by alpha sort...)
As well, there are servers and players all over the world, and this takes time - for transmission and confirmation (ack or nak).
That's why it's not immediate... organizational design considerations, and communication time.
PS: The same design protocol (cousin) is used in GbG, which doesn't show it's pairing EXACTLY @ 8am either. In fact GbG has a shorter lag opening, because I think they start pushing to clients from DIAMOND down to Copper.