It's not that good idea, in my opinion.
Current number of qualified teams is determined partially because of easier organization of second phase of tournament, I guess. If you just want to increase number of qualified teams, you couldn't do it with existing tournament organization that easy.
1) If you would like to keep all-play-all system you would need to increase number of matches and that means you would need to play 2 games in one week at some point.
2) I suppose you could increase number of groups in second phase from 2 to 4, but then only the first team from those groups would go in the semifinals. Also, if you increase number of those groups, you would have 2 second-phase groups with 2 teams that won in their first-phase groups. So you would need to decrease number of groups in first phase from 6 to 4. That doesn't look nice to me, 4 groups 12 teams, first 6 advancing to second phase.
3) You could lose all-play-all system, I guess, but in that case, every season would have teams who complains that their schedule isn't fair, that it is harder than someone else's.
I mean, yeah... Maybe we could get some new feature to break this monotony, but with your suggestion, maximum we would get, is a little bit of shuffle of group sizes and nothing more. I don't think that admins are willing to change core of their tournament organization.