Why is there a low pass filter in a DSBSC demodulator?
The third graph contains the demodulated signal (blue line). It clearly has two frequencies in it: a low frequency (of the original message signal) and a high frequency.
One method to get the low frequency message signal out of the combined singal is to use a low pass filter.
A peak detector would not work with suppressed carrier signal since you need a valley detector for the negative half cycles! (Look carefully at the demodulated signal (blue line) from 6 s to 12 s time duration. The message signal is hidden in the valleys not the peaks!)