Even ignoring the square-cube law, it's just a really bad design. If you look at modern main battle tanks, they have been getting lower profile. This is for the simple fact that not being a massive target sticking up from the terrain is a really useful feature. Even then, they often use terrain to try and lower their visible profile further. Add to that all the complexity of making legs and arms work, and it's begging for a stealthier vehicle to drop the mech with a 105mm penetrator to the knee.
Patlabor addresses this somewhat. Bipedal mech started as a way to rapidly rebuild Tokyo after a massive earthquake. They became so ubiquitous, that regular people had access to them so between drunk/disgruntled construction workers and some bank robberies, Tokyo police had to add two divisions of "Patrol Labors" to deal with it. They're costly and annoying to everyone. The mech carriers are two lanes wide and no body likes giving them the right of way in traffic. After that, the companies making them diversified into military and meches have a limited roll depending on the terrain. Mostly swampy jungles with bad line of sights, so the legs are useful and the high profile a none issue. High end military models are very quiet compared to civilian models.
Didn't the original tabletop BT rules allow for mechs to lie prone for better accuracy and defense? And mechs that didn't have arm actuators had a penalty to standing back up?