Why aren't there 4-legged or 8-legged mechs?

I'm fairly new to Battletech and MechWarrior (just the video games). I assume it's mostly a style choice by the original creators, but is there actually in-universe reasoning behind it?

For instance, in the HBS Battletech video game, stability is a major mechanic that could be a reason for more animal-like mechs on the field.