Because full-blooded orcs hear the voice of Gruumsh all the time, making it literally impossible for them to react to emotional stress in any way other than violence. Half-Orcs can control their rage and act civilized if they want to.The point about Half-Orcs/Orcs is that, in a practical sense, they are the same thing. In a culture that explicitly rapes and pillages all the time, the chances are that most of them come from some bastardised background to one degree or another. Why create an artificial division for flatly no reason whatsoever? If people baulk at the idea of playing Orcs as a straight Race, then why single these out and not Teiflings, Drow and Dragonborn? (All of which are listed as optional, or ‘uncommon’ anyway).
If you actually read the descriptions of the two races, the differences are very clear and stark. You can keep saying they are functionally the same, but it's just not true. In particular, the idea that "all orcs probably have mixed heritage" is explicitly countered by this passage in the MM:
When an orc procreates with a non-orc humanoid of similar size and stature ... the resulting child is either an orc or a half-orc.
That means, aside from the very clear physical distinctions, there is some genetic boundary that makes you one or the other, never somewhere in between -- otherwise, all crossbreeds would be considered half-orcs. (I hesitate to use the word "genetic" because the dividing line is more likely somewhat magical in nature, but you get the drift.)