So, I can see both sides of the fence. I love that there are so many horses at Nationals, and a big part of that is the qualification requirements (or lack of them). Remember, when it comes down to it, more entries make the show profitable, so by being able to enter more classes, that definately helps the overall balance sheet of the show. For youth and ammy, I wouldn't change a thing.
However, I agree that in open, you should actually have to SHOW in the national class at a local show, and also show in the same division at nationals that you showed in locally. I know this would be tough to track without a system capable of it, but really, we can see what classes horses showed in on the results page of the website, so I would assume that you could at least check that? And maybe not full checks, but have exhibitors sign that the horse is qualified, then randomly spot check (and yes, that can be done in an unbiased way, you just take a statistical sampling method and apply it to the exhibitor numbers, let the computer randomly generate the numbers to check, and check them to see if they exhibited in that division - typical sampling number for most statistical methods is square root of n plus 1 where n is the number of entries). That would make it less work. If you found someone who wasn't qualified, harsh penalty (similar as for random drug testing). If someone wants to protest a horse isn't qualified, put down their money like any other protest. Doesn't seem to tough to figure out.
THEN, if that doesn't drop the class sizes a little, deal with the split sizes and scheduling. I saw 33 horses in one class - no way were judges able to judge that one well, no matter how hard they tried. It was just too big (and not terribly safe either). When they have 2 sets of judges, one for halter and one for performance, each set of judges will at least get a break on the days where part of the day is halter and part is performance, but the show management still doesn't get that break. And the youth and ammy judges don't get a break at all (although they don't judge as many days either.) No matter what the solution, someone will be upset. Adding days, adding a second ring, etc. are all possibilities, but each has benefits and drawbacks. Personally, I wouldn't want to be in the shoes of the show organizers, they are in a "danged if you do, danged if you don't" situation.