What I dislike so much is that the fighter class only models one archetype of the fighter. Spear master? Swordsman? Archer? None of them (and so many more) are truly represented by the class.
Apologies for the hyperbolic comment, but to be honest, the level of detail in D&D is set at a much lower bar than you are suggesting here. Basically shaolin master, capoirist, kickboxes, savatte all strike unarmed, judo and pankration wrestlers are (presumably) grapplers. They just have different flavour text. Is the flurry of blows a sudden cartwheel attempting two kicks on the bypass (capoirea), two rapid punches (karate) or a knee to the groin and a headbutt (bad-ass brawler)?
Its easy with the current rules to make an archer, spear master etc. With the DCv1, you can even make a polearm specialist feasible. But martial artists are underrepresented.
While you're correct that many martial arts I mentioned are primarily unarmed strikers, each has unique weapon selections and techniques that affect the way the practitioners fight that could be modeled within the game. Its not all fluff and flavor text.
The Shaolin monks did an exhibition at the Bass Hall in Fort Worth recently, and not only did they show off their leaping and unarmed strikes, but they also did some work with weapons, including some bladed polearms (spears & naginata) and other weapons entirely absent from the current monk list.
Capoira and Escrima were designed to be practiced in plain sight as a form of entertainment - hence their designation "hidden." In each case, the practice was to be entertaining to the observer. However, Capoira was designed to be fully usable when the master practitioner was in shackles, even to the point of using the shackles as weapons
while still bound, while Escrima actively teaches the art of improvising weapons from everyday objects.
Other martial arts concentrate on chain weapons, disguised weapons, etc. And the Monk class as written (like it though I do) does not model such concepts at all.
(Can you work with your DM to rectify that? Sure...assuming you've got a DM willing to work with you. While I have played with many good DMs over the past 28 years or so, most have been loathe to modify classes to fit a PC concept- you either use the class as written or try something else. As with all things, YMMV.)
The School system could be as simple as having 3 schools: Strikers, Throw/Disarm, and Grapple/Bind/Break...and if you wanted, you could even subsume the Ranger's 2wf and Archery "combat styles" into this system, giving
them more options. Each school would have different bonus feat selections, class skills, and special class abilities- say, a cafeteria list of 10 class abilities for each School, and the player gets to choose 1 ability every 5 class levels, virtually insuring no 2 PCs would have the same class abilities.
Those abilities could be completely unique, or they could be as simple as getting additional benefits out of certain feats- like the way that Monks & Rangers can qualify for certain feats without the prerequisites.