That might be a reasonable why... The organization is dedicated to keeping the secrets of the Walkers. That is their whole purpose. I have two concerns with that, though. First, how could one of those children be born without the secret being revealed in the first place? I can't imagine that the Walker children are born disguised. Which would mean, that as soon as the child was born the secret would be "out." Also, sure, rape, but still. Why would one of the Walkers want to have sex with a human? Don't the Walkers kind of consider humanity... the bane of existence? Also, as a slightly more major problem, why would that mean that the Organization members have to get killed? They know their job. They'd do it if they need to. Or, at least, not all of them wouldn't do it...
What I could see, though, is having a group of Walkers who are looking to purposefully expose the presence of the Walkers to the humans. Probably in some sort of massive conquest thing. A kind of Cult, dedicated to having the walkers rise above and take control of the "inferior" humans, who only rule through population. And perhaps they have some messed up sort of magic that can do some minor mind control. Which is why everyone, Organization members included, was killed. Because they succumbed, and turned traitor. So one of the powerful higher ups ahd to come and personally clean up the mess. But, of course, that didn't end the Cult. It could be one of the recurring problems, if we like. And, for one reason or another, our characters are directly connected to it. Either because they can resist the mind control, or they are literally connected to it, or someone simply decides that they are the two for the job.
Why would the Organization not pay well? And, perhaps even more importantly, why would people who are very rich, and are therefore used to living in luxury, hire on for a job that doesn't pay well, that requires them to obey all orders, and, if they don't pay well, probably doesn't have a high standard of living? It is completely counter-intuitive. Frankly, the rich go to where they can make more money. And maybe the Walkers are different, but it still seems backwards to me that they would go and work. especially if they are rich enough and influential enough that they could probably get a job anywhere they wanted. Also, the fact that they live a long time would mean that there would be less workers, not more. A longer life span means less children per year, which means less children who would be of the right age to work in the Organization.
I don't think the number of employees would really go down with time. Yes, there may be less problems, the Organization would have control. But the more control there is the more dissent there will be brewing just under the surface. As soon as it starts looking like the Organization is weakening in power, people are going to try and rise up. If the presence of one of the Enforcers is enough to calm things down, that still means you need an enforcer at every dispute, and I can't imagine that the frequency of disputes is going to have gotten any less. Think about America. We have the strongest military in the world, but we have to constantly work to keep growing it, so that it still looks like we could whup your ass in a second if you step out of line. I don't think the Organization is looking for a point where they can just kind of... fade out. They are the power, and whether they are a good power or a bad power is beside the point. They are going to want to stay in power.
What I meant by “Money, protection, a chance to have a position of authority,” ... Think about America again. The reason so many people work in the Government, whether they like the government or not, whether they like their job or not, is because it pays well, because it is a very stable job, one that they are not likely to lose, and it has very good benefits. Seeing as the Organization is pretty much like the government of the Walkers, why would it be any different? Besides, many of the downsides to a government job, like the fact that it is incredibly inefficient and many people are lazy, would be removed because of the strict control within the Organization itself. Even if the Walkers don't like the Organization, if they see it as a cruel overlord, there are still going to be people who will go and work for them. Maybe their family is sick, and they need the Organization to pay for whatever substitutes as Medical Bills. Which the Organization would probably only do for employees. Maybe they want to be close to the "boss," so that, if or when things go bad, they will be on the "winning" side. All I'm trying to say is that, just because the Organization is disliked, doesn't mean that people won't still go and work for them.
I think I got everything... let me know if I missed anything you'd like me to expand upon.