Actually if you combine groups with a little pre-seeding, it could work it well balanced without getting boring:
Pool A: Top 15 Qualified Teams (going by World Ranking) + Last Years Winner
Pool B: Top 17- 32 Qualified Teams
Pool C: Top 33 - 48 Qualified Teams
and so on
And each Group gets only one Team from Pool A, one Team from Pool B, one Team from Pool C...
This pretty much limits the "lucky draw" problem, and by climbing on the WR scala you can make your way to "easier groups" and better seedings, so even the "worthless" games gain some value.
After the groups stage, you put the 16 Winners into Pool Winner and pair them with one team each from the the Pool Losers, and you might even make a whole bracket after the Group Stage useing the best Winner Top, 2nd best Winner Bottom, and so on ... without drawing alot.
Zwei Dinge sind unendlich, die Dummheit und das All...