but what happens when it goes to MA, PHD for base level?
I would say that to some degree this has already started. If more people choose to obtain BA level educations, it will become more widespread. After that, some new filter will have to be found. It doesn't necessarily have to be education-based. Education has just been the easy target so far. But perhaps the educational institutions will accommodate by offering increasing levels of education, or maybe you'll need multiple degrees to even be considered?
Also what about trades like training?
Many trades built their own filtering framework outside of the university setting, typically through apprenticeship programs. From what I gather from those industries, there isn't a huge fight to fill the available spots, so it seems to serve them well. If, in the future, more people want to enter those industries, you might need a degree before you can start apprenticing as means to filter the number of applicants again.