The main effect of that button is blocking the measurement of whether your ad click turned into a purchase, which is important because pricing ads based on conversions is more efficient than charging for impressions or clicks.

“Relevant” ads are sort of a red herring. Ad personalization matters, but commercially it’s less important than conversion measurement. Notably, Apple asks for permission before showing personalized ads, but never asks for permission to track conversions (while blocking competitors from tracking conversions by default).