[@Sierra]

What you described in the [b]Arbitrary[/b] section is more of an MMORPG than a tabletop style. MMORPGs tend to gravitate to numerical values for comparisons, so that X can never beat Y no matter how creative if their stats are vastly different. On the other hand, a tabletop like D&D let's say, has a different balancing, it offers a set of game mechanics with which it sets the logic of the world, and allows the players and the GM to be on the same page as to how things work. Ultimately, it's the GM (and the dice rolls) who decides the outcomes of each different scenarios. It [i]is[/i] more limiting in a sense than what you described in your [b]Nuanced[/b] section, but it sets a logical limit in my opinion: a farmhand fresh out of the fields has no chance to beat a dragon with a sword (Low level player vs High level monster), but a skilled veteran can contest it, although not alone unless they are incredibly overpowered compared to the setting.

In a D&D type of tabletop game, the storytelling and RP is collaborative, and in my experience that really helps flesh things out, while the game mechanics are there to supplement the storytelling and not limit it. No one (at least not of a sane mind) will intentionally miss with an attack or fall into a pit they didn't want to fall, and the game mechanics allow for such antics to happen, but it also allows for unexpectedly epic moments to come into the limelight, like a makeshift plan working way better than it should be. 

For example, a lone bard going in to a house full of hostiles, where he would likely die after his first round of combat, but instead turns the whole situation to his advantage with clever thinking and lucky dice rolls, eventually having a showdown against the boss of the scenario on the rooftop whom he has next to no chance of beating alone, but he pushes him down from the roof with a Bigby's hand, sets the house on fire and Dimension doors out of the place. All this accomplished even though he went there just to provide some distraction so that the main party could do their thing.

Of course this obviously also relies on the players and the GMs, so each experience might be different, I'm just trying to point out that it is not as binary as you would make it seem, just because there are mechanics to follow. But I do agree with you, and I think I mentioned this earlier, that a simple numerical growth and comparison would be very limiting and boring.

PS: Just to nitpick here, [b]arbitrary[/b] means that it is not following a clear defined system, instead opting to go for personal whims, so if it is clearly defined and makes comparisons and balancing very easy, it -- by it's definition -- cannot be arbitrary. How the rule-set was established can be arbitrary, but it cannot be applied if you are talking about the system. I'm just poking you, sorry. :P