What about just requiring that schools screen primaries! This seems like a better option to me. No sense in wasting everyone's time and money filling out secondaries when they would just screen you out anyway. The only reason to do this, it seems, is to collect the application fees -- which can be substantial! Multiplying the secondary application fee by the number of people who filled out secondaries last year (according to MSAR) would have most schools taking in $500,000 to over one million dollars PER YEAR, only to end up rejecting the majority outright. Do they really need those secondaries?
This is not just my opinion. My genetics professor was a professor at a med school and served on its admissions committee for about 10 years, and he also thinks it's almost criminal that they automatically send secondaries to everyone, whether they would consider them or not. They already get a piece of the AMCAS fee, which should be enough for the pre-screening that they would do on the primary.
Loyola and Wake Forest, at least, have some dignity in this regard. They actually screen primaries. Kudos.
Edit: This would help poor applicants, too, since the primary application is cheaper and it would mean that getting a secondary actually meant something, thereby justifying the added expense.