Because it's not a level playing field. The split is for playoffs only. Therefore, schools like VC and AES spend all regular season beating up on small public schools like Gueydan and Centerville, then go off to do their thing in the select field of the playoffs. The 1A public bracket, meanwhile, includes an inane number of byes for top seeds because they can't fill a bracket because teams that are winless are asked to participate (Gueydan, for example, turned down playoff bids for two years because we were winless the first two years of the split before making it as a mid-seed last year with 2 wins). That waters down the product to the point of it no longer mattering.
In my opinion, the answer is to give fewer trophies, not more. There are pretty much two solutions: one, private schools form their own association, play their own regular and postseasons, if they want to recruit openly, go for it. I'd have no problem with that. Option two, totally redefine the class makeups and districts. 1A grows a bit to include the smaller end of what is now 2A, 2A grows to include the bottom half of current 3A, 3A grows to include about half of what is now 4A, 4A grows to include the rest of 4A and the majority of 5A. You then create two optional "open class" divisions for people that want to play up or against more elite programs, one for smaller schools that would include schools the size of current 1-3A and all private schools of that size, and one for the "big boys" that want to play up in competition, public or private, the size of 800+ students on campus; I'd also be alright with letting the open class schools - whether public or private - be open in recruiting as long as there were some guidelines in place so it's not the wild west. So basically, classes 1A, 2A, 3A, 4A, and let's call them Open Class A and Open Class AA. 6 championships; districts, regular seasons, and playoffs happen by class (so the 1A public schools wouldn't be in the same district as the private schools in Open Class A, for example); and you still provide a split, but you also eliminate a classification and grow the other classes so that you aren't forced to water down a bracket with low-to-0 win teams just to have a playoff.
You may not agree with that, and that's fine. But at least the way I have it drawn up in my head, it would make sense and serve as a good middle ground for those who want championships to mean something while still splitting off juggernauts into separate classes to appease those principals who want their programs to make the playoffs and have championship hopes, all staying under the banner of the LHSAA.