A hybrid form of balance that combines Rarity & Fiat- lets call it
Balance by Excision- is a common feature of homebrews.
By that, I'm referring to DM's who simply excise elements of the game that they don't like or don't fit into their campaign world. Paladins and Monks are quite often a target for this kind of balance, IME, even though the downsides to playing the class are often enough to keep them rare. Certain spells also get this treatment.
Just goes to show: the desire to play cool concepts (including "rare" classes like Paladin) will tend to corrode Balance by Rarity.
Depending upon system.
I haven't looked at it recently, but the first version of Stormbringer- a Chaosium game that modeled the world of Michael Moorcock's
Elric stories- had races/nationalities that varied wildly in power. This was done in an effort to preserve the flavor of the setting.
Your PC's race was randomly determined.
Melniboneans were the most powerful race in the game, so there was only a 2% chance of being one. Pan Tangians were next in power, and there was a 4% chance of being one of those. Similarly, the less evolved races were just as rare. The middle 70% of the race chart were varied in capabilities, but roughly equal.
That power, though, was tempered. Magic in the game was basically limited to summonings and bindings. You could summon supernatural creatures to aid you, just like in D&D, but you could also make magic items by summoning those creatures and binding them into particular items. (Which, BTW, was pretty much the
only way to make magic items in the game.) This meant there wasn't the same kind of overwhelming battlefield control or mass "I WIN" magic in the game. The closest you could get to a Fireball, for instance, was by summoning a large Fire Elemental...and if you were powerful enough, you could bind it into some kind of grenade like item. (Think of a really nasty vial of Alchemist's Fire...or Wormy's demons bound into spheres that he used for billiard balls...)
I've been in games in which the die rolls favored rarity- 2 Melniboneans and a Pan Tangian out of 6 PCs made for a party that was running roughshod over the world. But it wasn't because the 3 rare PCs were winning every encounter on their own, it was because they equipped themselves and their partymates with the best equipment possible. In a sense, they were like a tank battalion fighting harbor seal pups.
OTOH, a party which had NONE of the rare races faced a different challenge. For them, the world was grim & gritty, and magic was something OTHER people had...until they
took it.