Traditional: i.e old sifu to young student. if it's not homegrown or organic in lineage (NOT mainstream), if privately taught and exclusive, why include a belt unless you want to branch out and don't really care about quality.
Okay, cool, thanks for that. Small history lesson for you... as well as an overview of what ranking was actually designed to be, largely from a Japanese point of view (considering that's where "belt ranks", "black belt" etc all come from... Chinese systems that you're referencing will be included, but to a far lesser degree... hopefully you'll see why).
Let's start by looking at the various forms of rank, and how they have been developed, what they represent, and why they are applied. In essence, there are three approaches that can be considered "rank" (although technically only two are... they other is more akin to a title, which is linked to, but not actually, rank itself). These are Menkyo (licensing), Dan-i (level-development), and Shogo (title).
The first (oldest) of these forms is Menkyo. This form of ranking is common in classical arts (Koryu), and in it's simplest sense, a method of licensing students at various stages in their progress in a school, to ensure that there is consistency in the transmission of the information and methods. While this concept varied in execution from system to system, with more or less licences gained, and differing levels of authority allotted at various levels (for example, some systems would give teaching authority at a mid-licence point, others earlier, and others only when achieving the full licence level), the basic idea was the same; a student entered a school, and over time would be awarded a junior, then middle, then high level licence, eventually a full licence, indicating that the student has learnt all the lessons of the school.
So what does this ranking mean? A Menkyo licence indicates the level to which a student has progressed through an education... it can be seen as similar to graduating from various levels of schooling; kindergarten, primary school, high school, university, post-graduate, PhD doctorate. The advantage is that one can get a sense of the level of education (in a school) that a person has attained... but their application of that knowledge is not guaranteed. To put it another way, two people who have graduated from the same university aren't necessarily going to have the same ability to put their education into effect... which takes us to the second major approach to rank...
Our second form of ranking is the most commonly thought of when discussing this topic, and is known as Dan-i ranking. This is a modern form of rank, originating in the Kodokan (Judo) in the late 19th Century, and is represented by a number of coloured belts in most cases. This approach to rank divides itself into two major groupings, kyu (student) grades, and Dan (senior - literally: levels) grades, each then further subdivided into a number of degrees, counting down for kyu grades, and back up for Dan. While it's not uncommon to have 10 subdivisions each, there really is no standard, and is dependent on the organisational body in question. Unlike a Menkyo system, though, the progress through the ranks here are less about knowing the systems syllabus, and is instead about applicable skills. It's original application in Judo is based on the performance of the individual in competitive bouts, and once you have reached the first of the Dan ranks, you have often learnt the vast majority of the curriculum and methods of the school in question... in fact, by Sandan (third dan), you've reached the virtual pinnacle of technical knowledge, and from that point onwards, most rank is tied to the practitioners contribution to Judo itself.
Over the course of the beginning to middle of the twentieth century, this became almost the "standard" of having standards... being widely adopted by pretty much all modern martial arts, whether Japanese or not. Karate (Okinawan), Tae Kwon-do (Korean), and more have all adopted the idea of coloured belts divided up into kyu and dan ranks (gup and dan in Korean arts), and even many Chinese and Indo-chinese arts have adopted similar ideas, often incorporating various colour "sashes" into their systems to indicate rank and development... even giving them the image of being "traditional"... but the reality is that they are a modern adaptation, or even a modern alteration to some older systems. Even the approach used by Judo, where the concept originated, has developed much further from it's foundation, and further from the way it was first implemented by Kano-sensei.
So what does this ranking mean? Ideally, a Dan grade is about how well a student can apply the lessons of their art (with the kyu grades showing how much of the system the student has attained skills in), although the ways of measuring that can obviously vary greatly from one art to another... and has a more realistic application in modern sports-based arts. In this sense, the higher ranked a practitioner, the "better" they should be in applying said skill... but it doesn't mean they know much... only that they can apply it. Of course, this is only up to a point, as with age and injury, physical skills can begin to diminish (which is why Judo tends to "rank out" at Sandan on a physical level). Beyond that, it can be more political than anything else... which is also where the third form comes into it.
The third form of ranking is typically applied in conjunction with Dan-i ranking, specifically at the higher Dan levels, and are known as Shogo titles. These titles are a synthesis of the two previous forms, being able to be attained only with the appropriate Dan grade, while also granting certain authorities and responsibilities, similar to the licensing of the Menkyo system, affording teaching authority, up to governing authority in some cases. This form of ranking was initially designed to be applied after exhausting the Dan grades, when the highest rank in the then Dai Nippon Butokukai (which would become the Zen Nippon Kendo Renmei) governing early Kendo (still referred to as Kenjutsu, or Gekiken) was 5th Dan. The titles are Renshi, Kyoshi, and Hanshi, with some organisations also adopting Shihan as an entry title (although not officially a Shogo title), with each conferring teaching authority and hierarchal seniority.
So what does this ranking mean? Shogo titles are used to grant seniority at high Dan rankings... although they exist separately to the Dan system, meaning that a practitioner can be a relevant Dan grade, but not hold the Shogo title, it is not a situation where one can hold the Shogo title without also holding the relevant Dan grade. At this level of Dan, however, a practitioner is, by definition, much older, with age requirements also coming into play with Shogo, so they might not be able to consistently perform as they did when younger in competition... so the Shogo titles are ways of rewarding and acknowledging other skill development, such as teaching, mentoring, organisational skills, and contributions to the art.
As you can see here, "traditional" rankings are not dan grades, belts, or anything similar... and the idea of a belt being "traditional" is a common, but not accurate one... especially when applied to non-Japanese systems who have simply adopted their approach, or at least adopted a facsimile of it.