As I understand it, ERPs can be reliably identified only after the noise (inherent to EEG signals, regardless of the task used to evoke the response) has been largely removed, which is done by averaging across multiple repetitions. The ERP in that case is a recognisable-enough pattern in the EEG signal that it can be reliably pointed out in a graph of the averaged trials, for several electrodes, for instance:
Question #1: if the averaging method is trustworthy enough - assuming enough-many reptitions - to make noise components cancel each other out while leaving reliable effects still in, then why are other non-zero sections of (ripples in) the EEG signal also not defined as ERPs, with some attached meaning (e.g. response to some cognitive task), since they have, after all, survived the same denoising procedure? It would make sense to trust the EEG signal to really not reflect any effect when the intercept (y) is zero. However, in most EEG plots this seems to (very conveniently!) only happen at the t=0 point. The signal then becomes non-zero but only part of is acknowledged as an ERP, whereas the rest seems to be considered noise even though the plotted signal has been denoised.
EDIT: Question #2: why do such ERP plots - obtained by averaging across repetitions and across subjects - never (in my experience) show a confidence band to show the extent of that cross-repetition/-subject variability? Would that information not be of interest?