When I first saw the beta for DCC RPG I wrinkled my nose at the concept of race as class. I am accustomed to allowing any combination of the two with obvious synergies between certain mixtures. I fought my tendency to change this rule and have been running DCC RPG rules-as-written (mostly) since then. Having spent the last few months with this game, I realize race as class is a key part of the pulp fantasy world.
Recent editions of the world's most popular roleplaying game, which do not have these restrictions, are not pulp fantasy. High fantasy implies a world with much more stability and where knowledge is not so scarce. Each civilization is thriving to some degree, and, though adventurers are rare, they are not so rare that you cannot find representatives of every class archetype for most races.
Really, that's what this whole issue comes down to: archetypes. Humans in a pulp fantasy world have no archetype, which is why they have more class options available (though often less than their high fantasy counterparts). The other demi-human societies do have archetypes though, which is why they fewer or no options in regards to their class.