No. Several games from my personal experience.
Coral Gate, one of the game systems I played, allowed players to choose from several races (Human, Elf, Dark Elf, Light Elf, Dwarf, Dark Dwarf, Water Troll, Barbarian), and had to reward players for choosing to play Human. Other races had special abilities, interesting story-arcs, interesting traits, but also had weaknesses, but the non-Human choices were more attractive. Human characters were just so plain, compared to all the extras (even balanced with weaknesses) the other races had.
Everhate, another game system I played, allowed players to choose any of several races (Human, Elf, Dwarf, Truell, etc), but all characters were all raised dead, not zombies, but tainted living, called necrites. These necrites could become undead by allying themselves with more powerful undead and necromancers. Most characters either started non-Human, or chose to become undead. It was an interesting game and story-arc that lasted for several years. No complaints about the scarcity of Humans.
Bunnies and Burrows - had to mention it.