What Santorum seems to be asking for is already the way public schooling works in Japan (PTAs are some of the most overwhelmingly powerful entities in the entire superstructure of Japanese civilization and in places other than the big cities more often than not run the entire community outright, except when the post office does), and I would defy Santorum to find any public school in Japan that is closer to his ideological specifications than the ones in the United States.
So, how do those school perform relative to American schools?
That depends on one's definition of performance. It's generally considered to be better, but it should be pointed out that the Japanese school system is profoundly, profoundly different to the American one in general. It has much more in common with the (old) British system, including emphasis on a series of entirely nationalized tests, taught by an entirely nationalized faculty and staff. The 'T' in 'PTA' has much more direct ties to government policy than in the United States. That's part of
why they're so powerful, since they function as fora for direct interaction between parents and agents of state power in education.