You seriously underestimate the potential of railguns, and I'm not talking science fiction either.
You seriously underestimate drag, turbulence, and energy. That's why you're talking science fiction when you claim it's perfectly plausible that a robot with a miniscule gun on its arm could launch a nuclear warhead across a continent (nevermind that it still has no advantages over a sub). A railgun projectile the size of the one Rex could launch at the sort of speeds it would be capable of wouldn't be able to travel for thousands of miles through the atmosphere, certainly not with any kind of usable accuracy. That's why ship-based railguns, which currently launch projectiles weighing only a few pounds, are accurate to hundreds of miles instead of thousands.
Remember, we're not talking about the general theory of railguns or the general theory of mechanical walkers. We're talking about Metal Gear Rex. Nothing about it makes it as formidable a weapon as they were acting like it was in the game. Rex's railgun is too small to launch a large payload thousands of miles, it lacks mobility to get within range of any important targets on its own, and it's too big to be deployed secretly.
Let's do some back-of-the-envelope calculations. A nuclear warhead powerful enough to level a city is going to weigh in the neighborhood of a ton. Let's say we want to fire it at a mere 13,000 mph, which is the muzzle velocity of a railgun tested by the Navy with a range somewhere on the order of 200 or 300 miles. Well, that's going to take at least 306 GJ of energy, since that's the kinetic energy of the projectile. And remember that energy increases the like the square of velocity. Sorry, Rex's little peashooter of a railgun isn't going to be doing that...that's assuming the warhead would even fit!
Sure, a railgun might launch something into space someday. But it won't be a 10-m popgun mounted on a smallish walking robot. It'll look more like the launch tower for the Shuttle. Rex isn't plausible. Even if it
were, it's still awkward and limited compared to a sub. I guess that's what you call bad mechanical design.