We are introduced to him as the connection between L and the outside world, and, as the story progresses, we also see Watari is responsible for carrying L’s orders as well as taking care of L himself. We see Watari as the liaison, the butler, the bodyguard and the assistant but we aren’t given a reason to explain this renewed inventor taking on those functions.
We are told, both in the original manga and in the L: The Wammy’s House One-shot, that Quillsh Wammy is a man of wealth. There is no reason keeping him from paying someone to look after L other than he chose to do it himself. And as we see when L arrives at Wammy’s house, he makes that decision soon after he is introduced to L. That is a choice we are left to explain on our own.
It could’ve been boredom. Watari is shown to be an old man; it’s possible he has seen what he wanted to see and has done what he wanted to do. He’s an inventor, a creative mind, and he could be following this unpredictable child to see what he would do. Surely, boredom could be a motivation.
But what does it say for his morality that he allowed a young child to go unpunished for beating up his house-mates and hoarding toys meant to be shared?
More than that, he actually rewarded L’s behavior, showing him attention and giving him whatever he asked for even when that meant taking a monetary risk.
Although curiosity born out of boredom could be the reason Watari singles out L, it doesn’t explain the reasoning that created the circumstances that allowed him to find a child like L.
After L, the point of, at least, Wammy’s House was to produce a successor and there is no explanation as to why the orphanages were meant to produce something in the first place. In that case, it’s more likely L was what they were looking for and not a random child Watari decided to entertain.
Considering Watari made the decision of establishing several orphanages after World War II, his motivation could’ve been to prevent another war, to find the one mind capable of intervening and putting a stop to such horrors. If L was the answer to the question he was trying to answer with his orphanages, Watari was looking for a kid capable of saying their own methods, their own morals, were just.
The idea behind his orphanages was grooming children who met a certain standard to become the moral compass of the world, and, by choosing this particular child to become the standard the other children should follow, Watari himself chose this child as the ideal one.
To make a choice like that, Quillsh Wammy had to be particularly confident on his own morality, his own sense of justice and his own intelligence. He had to be sure he was right, that was he was doing and the possible grief he would cause was worth it.
If Watari set out to find a child who could become Justice in the world, his resolve was not to raise children nor was it to provide them a loving home.
He established a system that allowed him to find someone he considered capable of being justice and provided this person with all resources required. He modified the system in place just enough to create another person based on the standard is first choice produced.
That being the case, we can say Watari considered the common good to be indubitably more important than personal well-being.
Watari forced the children under his care to abide by his own moral inclination despite their own desires but to do so believing in their own deductive skills. They were indoctrinated to believe they, too, could be justice, but only if they were the very best. Personal safety, personal happiness, mental health, physical well-being, etc… were not as important as the good of the majority, but the good of the majority was taught to them as a consequence of their own actions, their own inclinations, their own search for answers.
Not only was Watari morally irresponsible as he allowed L to do as he wished (choosing the cases and methods he pleased under the pretence of representing justice), he was also morally wrong on the orphanage system he created. If he thought the world needed a moral compass that he could provide, he, at least, knew his methods were condemnable enough he should keep them hidden.