Is it really true that the phone must be passively listening? The field of the payment terminal will induce current in the NFC-coil and that should be able to wake the phone as necessary.
But it also means they can't do the neat trick of paying with a completely dead (i.e. not even reserve battery power) phone that some early Android and Windows Phone devices could do.
Field-powered mode is possible in at least some NFC chipsets, but I suspect that Apple either values a consistent NFC range more than usability even with a completely dead battery (the amplifier that grants a significantly higher NFC range to Apple Pay obviously needs power), they see it as a security feature (reserve mode is capped to a few hours, I believe), or their NFC controller simply doesn't support it.