RebYidd23:
1. Opening new yeshivos is not efficient. Ask anyone who attempted to do that.
2. Specialized yeshivos for OTD kids carries a Pandora’s Box of other issues. It is difficult to create the proper environment, and the matching of a child to a particular setting is infinitely tougher. Again, ask anyone who runs such a yeshiva.
3. I suspect that you missed the entire matter here. To create a system that catches the throw-outs might have some redeeming value, but it circumvents the true problem. The real issue is that yeshivos have become exclusive instead of inclusive. That is inherently problematic. It was achdus that merited Klal Yisroel to receive the Torah. The continuity of Torah demands that achdus be maintained. If we mess that one up, we have a serious problem. Chinuch is extending the chain of Torah to yet another generation. Exclusivity challenges one of the foundation criteria. The problem is not just a single individual or a particular yeshiva. It is a system where this becomes the modus operandi. You are correct in noting that efforts to change the “system” are so difficult that doing other inefficient things gotta be easier.