Having multiple hosts leads to the need of pre-determined elimination bracket, because of the travel. And this gives some teams the chance to arrange their position in the group stage, depending on which path they prefer taking in the elimination rounds. And this has happened on multiple occasions in the last 10 years.
I want the draw to happen after the group stage ends. Still have the first play the fourth and so on, but draw it after the matches have been played. Then have another open draw for the 1/4 with the 4 best placed teams from the group stage, which have made it there, be seeded against the other 4 and then make it a bracket to the final. Much more interesting and not that hard to do!