I suppose it would technically be 3 stages... but really... who only enters the NHC each year? I think that has to be a minority. If you make the prequalifier competitions that are already established and existing it will not put much more (if any) strain on the judges in those areas.
I think your assumption that entries would not increase in these pre-qualifier competitions is not a good assumption. For example, we run a competition circuit here in the Midwest called the High Plains. If you (or your club) wins in one of those designated competitions you get points towards brewer of the year or club of the year. You better believe that A LOT of the entries in those competitions are because of the circuit it is attached to.
Let's say that my club's annual competition is already at 500+ entries. Imagine how many more
entries we would have if it was one of only a certain number of comps to be part of the 'pre-qulaifying round' for the NHC. 100? 300? Yikes. There just isn't enough support/volunteers to run that big of a competition.