Your theory that the other types want to be ENTJs because they admire certain qualities about them is flawed. All the types receive admiration at some point, and I see no evidence that ENTJs receive any more praise than any of the other types. Also, I can just as easily find a post where someone is praising ISFPs and by your logic this means that all the people on that forum want to be that type.
Here's a thread praising ENFPs: infp.globalchatter.com/messagebo ... php?t=1729
Does that now mean that all the people on that forum want to be ENFPs?
Just because I respect, admire or even envy someone, doesn't mean I want to be them. I admire, respect and envy Chris Cornell's singing voice, but that doesn't mean I want to be Chris Cornell, nor does it mean I want to sing exactly like Chris Cornell, I place too much value on individuality for that. It just means that I would like to be able to sing as well as him. The same goes for ENTJs, there are traits about them that I admire and that I'd like to be able to do as well as them, but that doesn't mean I want to be one of them. Even in the example you posted of an INTJ saying he admired ENTJs, the INTJ in question also mentioned how INTJs are better then ENTJs when it comes to self-understanding and self-awareness. Why you would use this as an example of a different personality type expressing an inherent inferiority to ENTJs is beyond me. Did you simply filter that part out because it didn't fit in with your belief that everybody wants to be an ENTJ?
And also, what does your theory make of ENTJs that profess an admiration for the qualities of other types? What if an ENTJ on this board said that they love the creativity of ISFPs, for example? What would you make of that post and why (if at all) would you treat it any differently from an ISFP professing admiration for the self-motivational abilities of an ENTJ for example?
Oh , and your theory that ENTJ are the most "admired" type is just plain wrong anyway. There are usually threads on all the forums about "which type would you like to be if you couldn't be your own type" and "which types do you like the most". On the NF forums in particular ENTJs don't come anywhere even near the top choices.
Regarding your arguments for the genetic side of personality, there's no sure proof either way but I think it likely that it works in the same (or at least a similar) way as other "mental" qualities. That is, that you will have inherited tendencies (like with mental illness, for example). Whilst your genes will give you an increased tendency to develop into a certain type, ultimately it will be your environment that determines whether or not you will turn out that way. That's why there are so many ENTJs in your family, inherited potential was combined with an environment that encouraged ENTJ development. If you'd been adopted out at a young enough age to say, an ENFP family that placed a high emphasis on ENFP qualities, you would have been less likely to develop into an ENTJ, despite your inherited genetic tendency. It still would have been possible, just less likely.
Therefore, as far as your plan goes, it wouldn't be enough to simply pair up ENTJs together, you'd have to control the environment to an incredible level of detail to avoid what we might call "pollution". Also, random mutations and latent recessive genes could still lead to other types turning up regardless of your efforts. What would you do with these random examples, should they occur? If you prevent them from breeding, you will have created an intolerant, repressive and unjust society, which is what you were trying to avoid in the first place.
And anyway, even if you could make the whole world just those three types you want, it would not guarantee peace, because all types have their bad eggs, including those three. For example, Stalin was quite possibly an ENTJ, and Charles Manson is quite possibly an ENFJ (etc. etc.).
As for your claim that ENTJs are the rarest type. That simply is not supported by the evidence.
As you can see from these sites (and others), ENTJs on average come in at roughly the third or fourth rarest. The rarest type tends to be INFJ.
Moving on, as others have already said Einstein didn't help create the atom bomb, he came up with the theory that was used as the basis for the bomb, but he had no control over how that theory was used, and that same theory has been used in many other more positive ways that have helped to make the world a much better and more informed place to live in. All the other types can produce examples of people that have contributed positively to the world and even if those individuals did things that could be described as negative contributions, they were only human and nobody who has ever lived has been perfect. This applies just as much to even the greatest and most wonderful ENTJs, INTJs and ENFJs who have ever lived too.
In your opinion, you haven't actually provided any real evidence to back that assertion up whatsoever.
As others have mentioned, INTJs love to be independent. There is absolutely no guarantee that they would follow the orders the ENTJs gave them. Also, ENFJs love to lead too, there is likewise absolutely no guarantee that they would follow the ENTJs orders either. In fact, I think it likely that the majority of ENFJs and ENTJs would end up fighting for dominance and the INTJs would attempt to secede from both of them altogether, thereby introducing war and conflict into your idealised world.
Plus, N types generally tend to dislike physical labour. You would therefore basically have to force people (through things like ballots perhaps, if not just brute force) to do things like construction work, for example. Unless you set up some sort of rota system they would inevitably begin to resent this, and they may well come to resent it anyway (they may be interrupted whilst working on a theory for example). Additionally, S types generally are capable of having more profound insights into improvements that can be made to physical systems than N types are, so progress in these areas would be slowed, plus they can also give new and unusual insight into areas that are more traditionally N territory, so progress would be slowed here too. And that's just the N/S divide, the same applies to the other letters too.
No-one uses just one judgement function exclusively, and everyone can learn to use the others more effectively. They will always have a preference for their main type, but that doesn't preclude them from making decision using the other functions. For example, I prefer to use Fi to make decisions, but that doesn't stop me from using Fe, Ti or even Te if I think the situation calls for it. The more mature and developed an individual is, the more comfortable he or she is with this fact and the more he or she does it.
That's fair enough, but do you then give money to charities that help homeless people out of their predicaments? If not your statement is a touch hypocritical isn't it? "I'm not going to give you money because you wont use it to improve yourself, but I wont give money to a group that can help you to improve yourself either. So I'm not actually doing anything to help you whilst still judging you for not doing anything to help yourself, despite the fact that you lack the means to do so".