However, the rest of BattleTech, walking tanks aside, is significantly more plausible. Indeed, the most "unrealistic" part of BattleTech is that 'Mechs are the kings of the battlefield because of myomer "muscles" that are strong enough for fast, reliable movement (leaving aside the "official" ranges, which are flat out stated in the first few pages of my rulebook here to be artificially truncated for gameplay).
They're no more a nightmare to move around than a tank, and probably actually significantly less so because there's only one "crewmember" needed to move it.
Hell, they probably wouldn't even sink into the ground like that at all. Modern tanks would have roughly comparable surface contact areas when considering that every point of the track on the bottom of the tank will be in contact with the ground at any given point on flat terrain, and tanks like the Abrams mass as much or more than the majority of different kinds of 'Mech designs, let alone the most common types. Some 'Mechs even weigh as little as a third as much as the Abrams. Hell, 'Mechs like the Catapult are honestly less likely to sink into the ground than their tanky counterparts simply because the feet of the 'Mech spread the weight over a larger area. Smaller 'Mechs like Stingers, Wasps, and Locusts weigh five tons less than your average Bradley IFV, which gets around on roughly ~4.5 square meters of ground contact (conservative estimate). Having a pair of feet that occupy ~2.5 square meters each isn't hard, and the Bradley has absolutely zero problems traversing rough or difficult terrain.
Admittedly I can't really protest the joints are weakpoints part, because that's true, but the tactical and strategic mobility of being able to step over a low wall or literally jump over a river, or navigate rough terrain without slowing down is not an advantage to be thrown away.
BattleTech 'Mechs may not be as practical as the Real World (tm), but they're a hell of a lot less ass-pull than indestructo-Gundam.