pre vs amp power cable question

would a linestage or phono preamp ordinarily "require" a smaller gauge power cord than an amplifier, where the current draw is potentially much higher?

for that matter, since an 18 gauge cord will pass more than the rated current draw of most amps (c. 2.5 amps? - please feel free to correct whatever misconception is implicit in this) - does an amp "need" a "bigger" cord than, say, a 14 gauge cord, which would seem to be sufficient overkill? Or is it more about unexplainable filtration effect or something else? Or size doesn't matter, all you can do is randomly experiment?

not that performance differences between power cords compared to the Romex in the wall makes much sense, but still...