I would argue that the only qualification for a good moral system is that it's true.
I would argue that showing the 'trueness' of any moral system increases its transmissibility!
Remember, morals are taught to each other. We don't generate our moral code out of nothing. A moral code, no matter how 'true', will not be followed if people cannot be convinced to follow it.
You'll see examples when I encourage increased asceticism in order to generate more charity: people will outright
mock this idea, and other will argue that it's just not a good idea. Now, I don't know if I'm wrong, but I really do think it's 'more good' to forgo luxuries in order to be more charitable (especially when we're aware of such desperate need in the world, and since money is so fungible). Despite my position probably being true, it's just not followed by others (or myself, as much as I should) because the idea is not properly transmissible.
We'll see similar debates in threads about vegetarianism or corporate governance.
So, a moral system being 'true' is a good reason to follow it. But the system must also be transmissible to get people to follow it: if no one follows it, how good of a system can it be?