BJJ is the best example, because they use colored belts and are reasonably consistent across schools. There's a value for the belt colors within a single school, too. While abilities tend to be reasonably consistent across NGA schools in my experience, there's not as much cross-visiting as you see in BJJ. The main use is within a school. By nothing but belt color, I can tell within a few techniques where a person is in the curriculum. That means when I train with a partner I haven't worked with in a while (or when I visit a school), I know what I can do to my partner (which technique he/she is ready to receive). It also means deciding what to focus on comes quickly.
You're look at it kind of wrong. I don't mean within an organization/governing body. I mean across the art, as a whole. An Aikido black belt in your school doesn't have the same standards of ability as an Aikido black belt from a different branch of Aikido. I don't mean your standards are higher or lower; I just mean the standards are different.
Pretend there's only one of each organization in my following analogy...
The standards of black belt performance in Kyokushin, Shotokan, Goju-Ryu, Uechi-Ryu, ad nauseum are different. One of Kyokushin's standards for shodan was 20 man kumite. If everyone who wears a shodan completed that, it's a good indicator of ability compared to the students' peers. I know, the quality of the 20 men you'll face varies dojo to dojo, but it's still a reasonable indicator across the board. Shotokan doesn't have this requirement, as the others don't either.
I'm not saying Kyokushin is inherently better due to this or anything else. I'm just stating that there's no standard for all karate styles. BJJ has a standard - tap out just about everyone ranked below you in BJJ, regardless of what lineage/school/etc. they come from.
BJJ rank carries the connotation that a brown belt can and has consistently tapped out the overwhelming majority of students ranked under him/her, and consistently taps out against people ranked higher.
Karate doesn't have that. The rank is looked at as an individual thing in most schools. There's far more black belts that can't hold their own in kumite against say 4th kyus in karate than there is in BJJ. What happens when a BJJ black belt taps out when rolling against a bunch of people ranked lower? It's all over YouTube, "exposing" the BJJ'er as a fraudulent black belt. What happens in karate? Just par for the course.
Looking at the various martial arts, the only ones I see constantly looking at rank as something compared to your peers are BJJ and Judo. No one I know of ever had to be better than 90% of the people below them to get promoted in karate. I never had to be better than 90% of the green belts in my organization to get promoted to brown belt. It wasn't like my sensei said "yeah, you know the curriculum, you're improving your skills appropriately, and you're a good student, but the green belts are consistently beating you, so I can't promote you to brown belt." Something like that would never cross 99% of karate senseis' minds.
BJJ is a different ball of wax.
Edit: I'm not saying BJJ is better nor worse. I'm not saying karate nor any other art should adopt BJJ's mentality. I'm not saying anyone should have to change anything. I'm just stating observations.