I use RC circuit to generate power-on-reset and fed the output to a scmitt-trigger-buffer input. I use the output of the buffer to power-on-reset four AT89C2051 chips.
The specification of a REAL supervisor chip (12323 et al) states that it will function from below 1V. Your schmitt trigger is not guaranteed at that low a voltage. Thus, you have absolutotallly no guarantee that your circuit will work.

Erik