My thought was that Haki blooms out of desperate combat and reliance on willpower as a trigger for initial awakening, similar to how we see Luffy using his COC in dire situations without even realizing. Coby likewise achieved access to his COO after sustaining enough war trauma. It seems like this goes against the principles of rokushiki. By becoming naturally superhuman through reliance on purely physical means, practioners don't ever really make use of Haki or come into the conditions to trigger it.
It's a flawed idea, but it would help explain why none of CP9 apparently could use it. It would please me to know that the martial art was like a train choosing between two tracks. So they never switched or had need to, even when faced with overwhelming opponents, because the training automatically deviated how Haki is utilized.
For instance, Kame. It allows the users to avoid attacks similar to COO for dodging purposes, but it is not in fact COO, something else entirely. So it therefore would be the first instinctive thing to do for a Rokushiki user. Similar moves like Soru, especially Soru, would further exacerbate this reliance on physical prowess instead of willpower concentration on listening.
Then we have Tekkai. If you are trying to naturally, as much as wuxia martial arts superpowers can be "natural", gain iron skin, I could see where Rokushiki instructor would actually try to avoid training a CP9 agent-to-be in COA, or Hardening specifically. If they just use Willpower, then their bodies won't gain that natural iron-ification skill that is Tekkai. And since anyone can learn COA, but apparently very few can learn Tekkai, it could be argued that the former is harder to obtain. Which makes sense. It's easier to gain willpower than to alter one's body to be superhuman, even in the OP universe. Otherwise Nami and Ussop would've done something by now to make themselves as strong as Zoro, for defensive means if nothing else. (Indeed, it is possible that Zoro is as durable as he is because he naturally uses a mobile version of Tekkai that the wolf-CP9 agent used. That would help with suspending disbelief in regards to his impossible feats, like having buildings crush him and then get up afterwards, or surviving such terrible sword-cuts. But I digress)
So for training, the CP9 were to learn the martial art first, without using willpower (Haki) as a crutch. Then they could master Haki as it comes to them naturally. None of the agents we saw were particularly old, and Lucci, Kaku and Kalifla are still young enough to be in their twenties, no? Seems that they would be introduced to Haki as needed, same as they did not receive devil fruits until it was considered a good idea to increase combat power in their ranks.
Another thought: martial arts training will involve willpower, obviously, in real life and presumably in OP Rokushiki. And Haki is also will based, but is expendable. It could well be that training both would deplete a person of their willpower/spirit and leave them too exhausted to improve rapidly. With Rokushiki it may be that is not good enough. Rapid and incredible conditions must be met.
Case in point, Sanji: he learned Geppou, but only while running from his worst nightmare. Worst nightmare, literally (other than all women spontaniously turning into Okama-baka). Imagine the desperation involved! Now just think of training as a child in all six forms through such desperate training. It requires intense concentration, which is linked to willpower. One would have a hard time doing both. And so they trained in Rokushiki, which requires harder and seemingly longer physical duress, leaving out the mental training or whatever normal non-MC character people have to do to unlock it.
Ah, I wonder if Brooke will be used to frighten Orochi. That would be an option. Then indeed he would be MVP again.