This is spot on and an argument that I have used for years. There is another poster on this forum who always says the public schools must teach "all of God's children."
Regardless, DI is not as big of a problem as many think. Yes, the Catholic schools have for the most part dominated but you do have your Pickerington Central's, Colerain's, Davidsons, and Huber Heights Waynes. Although Mentor never won they made it to the finals what? 4 or 5 times under Coach Triv? Even though, as you mention, the big Catholic's have an advantage the larger public's have a chance because they have enough boys to somewhat absorb that advantage.
My beef is with the urban Catholic/private schools that have clearly gamed the system in order to keep their doors open and use EdChoice as scholarships to prop up CLEARLY better football/basketball teams. I always use Toledo CC as an example. 220 boys grades 10-12 and 100 of them play football with DI kids all over the place. There is not a public school in Ohio that has 220 boys grades 10-12 that comes close to enjoying the talent and depth that TCC and Hoban experience. Competitive balance is working but does not go far enough to address these smaller private schools that as you say recruit the best and brightest from the local public district and leave everyone else behind.
As another example one only needs to look to Michigan where there is no EdChoice/voucher program and where the public schools have seen an upsurge in championships. Schools like Cass Tech, Detroit MLK, and River Rouge, have all won state titles in divisions that were traditionally dominated by Catholic powerhouses. Those powerhouses are slowly dying (Brother Rice, De La Salle, DCC, Orchard Lake St. Marys) and not experiencing anywhere near the success that they once had as a direct result of the death of Catholicism and no EdChoice windfall to prop them up.
And of course we are talking about two different entities here in the OHSAA and the Ohio Dept. Education but make no mistake about it, EdChoice has been a driving force in making matters much worse in Ohio.