Applications being assessed blindly is a bad idea in some subjects. Cambridge's Science and Mathematics students from state schools achieve, on average, higher marks on the Tripos' than those from the private sector with the equivalent A-level results (see slide 9:
http://www.study.cam.ac.uk/undergraduate/teachers/docs/student_conference_teacher_forum_presentation.pdf).This indicates a steeper learning curve for those from state schools in these specific subjects!
That may have something to do with it.
Read this (specifically the table as well as key conclusion 1):
http://www.admin.cam.ac.uk/offices/admissions/research/docs/prefective_effectiveness_of_metrics_in_admission.pdfThe correlation coefficients for the other subjects is around 0.4 and so the A-levels are difficult/relevant enough to make fairly good predictions. Assuming STEP's correlation with the other subjects would have been around 0.5 as well, they must've concluded that the difference was too small for it to be worthwhile.
Also, the workload for STEP is tremendous and so it is unfair to ask students to do it if it would lead to them having to compromise A-level learning significantly. The correlation for maths being so much lower than the others suggests to me that this is because people are clustering around full marks to a greater extent than with other subjects - meaning they find their subject easier - therefore it is fairer to ask these students to shift their workload from A-level on to STEP than it is with students of other disciplines.