One major problem is with 16 districts if you take the top 4, you end up with 64 teams in the 1st round of the playoffs: you just made it 6 rounds to the state championship.
This is true you have added one more week. I personally have no problem with taking only top two teams, that is the system I played under. However, you probably would get major complaining from coaches on the numbers. Also when consider you are only using 3 classes you have actually reduced the number of teams making the playoffs considerably, you could end the bye weeks and keep the same time schedule you have now. However, like I said top two would be fine with me. Seems to me to be a much more sane system if you use top two or four. Less travel in the early rounds and much easier to understand. Just appears to be a simple and reasonable fix to the mess they have created.