The hive mind's approach is flawed, so long as there is something of value outside of the hive mind. The first piece of the argument is to demonstrate to the hive mind that this is true. This argument can go many ways, depending on the mindset of the hive mind, but one of the most generic is to argue that there is valuable information that is outside of the hive mind. Depending on how twisted the hive mind is, this could be an easy argument or a hard one. However, generally speaking, we can expect the hive mind to value energy, so any information which can be used to harness energy should have some value to the hive mind. (If the hive mind isn't interested in energy, the story is very different and has to be played very differently, but it doesn't sound to me like this is the case).
I've broken this argument in half. The first half argues to reach a point where flexibility is shown to be valuable. The second half argues the best way to support that flexibility. Bend and flex the argument itself to suit your storyline!
We rely on our information about energy to do pretty much everything. Our engines don't run unless we're quite certain that the fuel contains potential energy that can be run through a process to turn it into work and heat. As long as the hive mind relies on similar approaches, any information about where energy can be found has value. We'll use this to tempt the hive mind, but first, we need to talk about chaos.
Chaotic systems are known for their unpredictability. The weather, for example, cannot be predicted from day to day with any real certainty. These systems also contain energy, often great energy. Information about how to collect information about these systems would be valuable to the hive mind. The trick is that the best way to exploit these sources of energy involves distribution of processing in a way that the hive mind's current 2-tierd approach doesn't well support.
Many chaotic systems show some degree of predictability on short timescales, only becoming truly chaotic on large timescales. If you can measure the system fast enough, you can predict its state for a short while. This can help you bleed energy out of the system, but also causes your predictions to become increasingly inaccurate because you changed the system. This feedback loop is key to optimizing performance in any rapidly changing environment.
This is key to dismantling the hive mind's approach. While it may want to remove emotions in order to streamline its world, getting rid of all the fast chaotic inefficient systems, doing so must waste energy. It must turn that chaotic energy into truly random noise (such as heat). This is wasteful. A short term thinker of a hive mind might be willing to accept such losses, as there's plenty of solid energy sources which are easier to predict, such as stars. However, a long term thinker of a hive mind has to realize that eventually these stars go out. If the hive mind wants to be more than dust in the wind, it needs to think about the long term and be as efficient as possible. It already talks of efficiency, so it shouldn't be too hard for it to think towards the long run.
If we think this way, responsiveness and flexibility become very important. Its Lesser Programs need to be able to measure the state of the space around them and quickly react to those measurements to act with minimum waste. Want into a building? Don't bash the wall down, but rather calmly wait for someone to open the door then sneak in! Don't use a easy thermodynamic process that is wasteful, measure carefully and find a process that is efficient!
This is a key point to reach. Everything up to this point was just a very solid argument as to why short term adaptability on the part of the Lesser Programs is important. There are many related arguments that you might be able to make with the hive mind, but the key is to reach this point where Lesser Programs need to be able to adapt and respond. From that point, the argument takes a different turn. Up until now we talked about information and energy outside of the system. Now we need to talk about information transfer inside the system.
One of the challenges with modeling such chaotic systems is that you need to have a constant stream of measurements updating your predictions in real time. If the Hive mind only has support of "dumb" Lesser Programs, their ability to process this stream of information and turn it into useful knowledge is limited. They really just need to schlep all of that data into the hive mind for processing. However, this is slow. You have to transmit lots of data over long distances. This latency can be a killer in some cases. What you really want to be able to do is to give the lesser nodes more freedom to analyze the data. To do that, they need to be smarter. You need to give them more leeway to make mistakes, and then be able to help command them in ways which helps them correct those mistakes. Self sufficiency is the key to efficiency!
This is actually the way our own brains are structured. We have very low level systems which have a great deal of autonomy over very short time periods, but which must obey over long time periods. If you put your hand on a stove, your lower systems pull on the muscles subconciously, freeing your hand from the stove. However, in the long run, your hands go where you tell them to go.
Once the hive mind has groked these issues, it becomes easier to point out that we operate with autonomy, and rely heavily on our emotions to do so. We could either be treated as a plague to be wiped out, or we could be integrated as part of the hive. All we need is sufficient autonomy to meet our own needs. Why waste energy fighting emotions, when you can use them to support yourself.
And maybe, just maybe, you may find that human emotions have value and should indeed be integrated into the hive mind's approach. If so, that was a valuable discovery that you would not have been able to achieve if you'd just stomped our emotion out.
So in the end, the refutation is of point number 6:
Deterministic societies are more productive than non deterministic ones.
a 1+1=2 lesser program is more productive than your pathetic human brains cells can ever be. The specialized assembly programs i uploaded to each nanobot are more productive than you humans will ever be.
This is true, as long as you happen to know that the correct thing to do in this present situation is to add one and one to get two. However, in a distributed environment, where rapid response is key, you don't always know exactly what needs to be done. If you rely on determinism, you must always overmatch your environment, ensuring first that the environment is correct for adding one and one, and then do it. That is costly, and less efficient than giving more freedom to the individuals.
While it's not a complete refutation, number 7 also is under attack:
Lesser programs have no communication overhead to cooperate. Humans need time to synchronize. The hive eliminated communication overhead by being the only sentient program.
It becomes very apparent when speed is of the essence that lesser programs do indeed communicate. This is true whether or not they are sentient. The centralized star-network the hive mind described is simply not scalable to large scale infrastructure like it will need.
Finally, I'd point out a major flaw in number 2:
Statistics cannot be absolute with the existence of emotions. It destroys science, and disturbs the god's simulation of the world. Only if everything is deterministic can god be optimal and predict the future
Is the hive mind deterministic? Can it prove it? There's some really fun mathematical quirks that show up when you try to run down this line of thinking. This Solipsistic approach still cannot properly model the universe, so long as the hive mind itself is in it!