A multiplier scales every sample by the same factor. That is fine until the loud parts are already near the ceiling: push past it and they clip into crunch. And doubling the numbers does not double how loud a track feels, because hearing works on a roughly logarithmic scale.
Normalize measures the whole file the way ears do, in loudness units (LUFS), then adjusts it to the EBU R128 broadcast target. Quiet recordings come up, hot ones come down, and peaks are kept from clipping.
Streaming platforms run their own loudness normalization anyway: Spotify and YouTube pull everything toward roughly -14 LUFS at playback. Blasting a file to 3x before uploading there just gets turned back down. Consistent loudness is what actually survives the trip.