I don't think that would work - those positions would go empty. People apply for grad school because they want to do original research. On the other hand, once people are already in the academic pipeline and they run into struggles advancing from postdoc to assistant prof or maintaining funding as an assistant prof, I think a lot of people would take a 50/50 grant if lets them keep one foot in the door for original research. They aren't going to turn their noses up at the only grants they are competitive for.
You do raise a good point that labs with 50/50 grants wouldn't have as good of a value proposition for prospective grad students as labs doing 100% original research. I'm not sure what the solution is there.