one thing, mister 'let's over-specialize our troops' - what happens if one of your specialized units is routed and thus does not support the rest of the army? Many battles have been lost because one of the specialized troops present was routed and the niche it was occupying became empty, thus leaving the army as a whole crippled. A good example is the first Athenean campaign against the Aetolians, where the hoplites were destroyed easily after the Athenean archers(which were the only thing holding the javelineers at bay) fled at the death of their captain(a discipline problem most likely related to the low status of skirmishers in Greek society). Another frequent scenario is when the archers get a flanking assault from the cavalry, get routed, and then the cavalry proceeds to hit the infantry in the back, or simply leaves it(now unsupported) to its own archers.
Because, sure, you guys use combined arms tactics, but if the A.I. was smarter, it would use them too!(completely on topic)
In which case you'd have a face off of almost equal forces and you'd have a tactical nightmare. Something I try to avoid by fielding versatile troops.
Why do I think that Vaegir marksmen and Rhodok sharpshooters are the best units in the game:
1. Decently armored(thus survive for a longer time)
2. decent athletics(due to their lighter attire they run faster than actual infantry units)
3. ranged capability(don't have to fear other archers as all my troops can shoot as well, and anyone approaching gets covered in shafts, which is better than any pike)
4. GOOD IN MELEE! Marksmen have a rather low-end PS value, but that's outweighed by extensive use of strong cutting weapons, and frequent use of long and strong cutting weapons(the Dacian falx and the zweihander come to mind, allegedly being good at splitting shields and armor and cutting pikes, respectively); while sharpshooters have a better PS value and use huge shields.
What happens when I field an entire army of shooty heavy infantry(because this is what these guys basically are):
Having an entire army of them(say, 100 guys), first of all, has a much more devastating effect than fielding one third of my army as archers(30, in this case). The barrage I get out of them is enough to dehorse most mid-tier horsemen(and almost all Khergits) in the middle of their charge. Additionally many horsemen get shot at point blank range when charging. And since those horsemen are part of a combined arms force, they're unsupported by their other troops, and grossly outnumbered by folks who are furiously hacking at them with sabers and long axes(it happens very often that a knight finally loses his war horse while in the midst of my troops, which simply spells doom for him). Basically, fighting a combined arms force is rather easy for me as they come piece meal and are thus easily destroyed. The only ones who give me hell in a field battle are Rhodoks, as they always move as a homogenic force, always at least half of them are ranged troops (who are also good in melee) and their infantry have big shields(much less vulnerable to missiles than cavalry) and long weapons(you mentioned the 'pike rampart' thing

).
Now, Nords and Rhodoks are supposed to excel at sieges. But they fail against my marksmen. Let's see why:
Nords/Rhodoks assaulting:
With archers occupying the battlements, the assaulting force receives an extremely intense barrage before reaching the breach in the wall, where it's met by the long axes(do you get the pattern already? long weapons...long weapons...long weapons... IT'S ALL ABOUT THE RANGE, as in 'who gets to hit first'). When defending against a 5 times outnumbering force of Nords, the only two times the Nords almost managed to overwhelm the wall were when a lord with a war axe(as long as a voulge, and quite more powerful, especially in the hands of a lord) managed to clear up the place a bit(1st time) and when, near the end, there wasn't that many defenders left, so the wall was becoming empty. Similarly, against a 2 or 3 times outnumbering Rhodok force, the only time I had to intervene was when a sergeant with a glaive actually managed to get onto the wall and started clearing it up. In both sieges I had fairly low casualties. Forest bandits are almost as good as marksmen and sharpshooters, as they're archers who tend to favor long axes and staves for melee.
In a siege assault it usually doesn't even get to melee - I just shoot the garrison off the walls. Only get trouble if it has decent archers(or in greater numbers) on the walls. Otherwise the infantry is helpless, only thing shields do is increase the time it takes me to slaughter them(finally bought fraps yesterday, need to find a compression program too, and I'll be able to post some vids, starting with the 'arrowstorm'). And if the infantry storms out, it gets butchered with the axes and sabers.
I have no idea why nobody thought of it throughout history, but I personally think that certain armies would have been much more successful and devastating if they were versatile(for example, if the English longbowmen during the 100 Years War were also armed with bills, instead of specifically having billmen for that, they'd be much deadlier).