In the original, unaltered game, maxing out your relationship stats leads to the infamous "Hot Coffee" minigame (which was cut content accessible only via mods or the "Hot Coffee" controversy). In the standard retail and definitive editions, high Sex Appeal ensures your girlfriend will invite you inside for a "coffee" (offscreen), which is the game’s way of confirming a fully maxed relationship. Without sufficient Sex Appeal, you will never reach this threshold.