Great Old One
I believe the reason creatures provide half cover is because they are not static hard object, but fluid cover. And rather than have more complex cover based on size, they opted for simplicity, creature = half-cover regardless of size. Afterall, a tiny or guargantua creature could motion during attack and either let pass the attack more or less easily somehow.
Yes, the main reason is that most creatures do not occupy their whole space and even a tarrasque has pretty thin legs.
However, that tweet it not official, the only official rule about cover is: "A target has half cover if an obstacle blocks at least half of its body. "
And that's it, the following sentence is, clearly, from the wording only a list of examples: "The obstacle might be a low wall, a large piece of furniture, a narrow tree trunk, or a creature, whether that creature is an enemy or a friend."
That being said, for the reasons that you outlined and I completed, I will usually grant half-cover for one creature, but I will apply the rule properly for unusual creatures and situations, such as the gelatinous cube who is large and occupies all of its space in 3 dimensions, or when the size differences are great, for example a rat and a tarrasque. The tarrasque might give only half-cover to a rat, because it's moving and lifting its legs, but the rat will provide no cover at all for a tarrasque. And that is 100% official.