The unity of the virtues is one of those concepts that puts people off from virtue ethics. To start with, it’s a bit hard to get your head around. And then it sounds like virtue is an all or nothing matter, utterly binary, with no progress possible in between utter vice and full virtue.
For all that, I don’t think the unity of the virtues—at least the conception of it I have become familiar with primarily through the works of Julia Annas but also to an extent through Deirdre McCloskey and others—should be cast aside.
Let’s start with intuition. What exactly do we mean when we say that courage is a virtue? There are clearly instances of courage, as the adjective is commonly used, that are not very virtuous. We don’t really think that the berserker, who is courageous in battle so that he may rape the women in a village and then burn the village to the ground, is an admirable fellow. Even for people who aren’t so clearly morally monstrous, a monomaniacal lack of fear that puts you and everyone around you at risk is definitely not virtuous.
In order for you to be truly courageous, in the sense of having a virtue, you must also be prudent, charitable, temperate, and so on. But in order for prudence to be a virtue it must not be a cowardly prudence, or a miserly prudence, or a prudence to the exclusion of all else. The virtues are a specific sort of character trait; and in order for a character trait to be a virtue the others must be present to some degree.
“Degree” presents a good bridge from intuition to a thought experiment. Imagine that courage is a substance. A scientist puts it under a microscope and upon examination finds that this substance is made up of a specific mixture of prudence, temperance, charity, justice, hope, and faith. The scientists increases magnification to get a closer look at the prudence that’s in the mix. To his surprise, he finds that prudence is itself a mixture of temperance, charity, justice, hope, faith—and courage! And what’s more, the courage inside of the prudence has the same proportion of the other virtues as the courage that the prudence is inside of! It’s virtue all the way down, a fractally nested full set of virtue.
Practical wisdom, Aristotle’s phronesis, is just the skill of discerning what the right mixture is for the specific situation you are in. Courage in battle looks different from the courage required to defend your thesis. Likewise, the prudence of Odysseus requires a different mix of virtues than the prudence of the corporate accountant.
The role of practical wisdom is also the answer to the perceived binary nature of the unity of the virtues. Julia Annas’ Intelligent Virtue argues that practical wisdom is a skill that must be learned and mastered like any other. But Annas’ formulation tracks closely with other well understood skills; there are levels of apprenticeship and there are levels of mastery. Virtue is not binary at all; we can make progress and we can continue to hone our abilities long after we’ve begun to excel at using them.
Binary versions of the unity of virtues do exist—the Stoics definitely believed that virtue was all or nothing, you were either a sage or you were not. But that’s not a conception of virtue that I find either realistic, practical, or appealing.
Sweet Talk 
This is why listing the virtues, though endlessly attempted and always fun – I’ve done it myself – is a fool’s errand. “Good character” = “the sum of necessary virtues” – that is all we know, and all we need to know…
We can speak meaningfully about specific virtues in the specific circumstances (or essays or stories) that they feel appropriate to bring up and describe. The only real way to do so though is to make reference to stories about people exhibiting those particular virtues—people in our lives, in history, or in fiction.
But yeah a complete list is a fool’s errand. Aquinas (and McCloskey following Aquinas) tried to do it by having a cardinal list from which all others were derived. But if you take the unity of the virtues seriously, I don’t think that approach makes much sense.
Always thought it comical that representations of the “Seven Virtues” on medieval cathedrals were invariably perplexing as to what they meant to show. (The “Seven Deadly Sins,” in contrast, were pretty clear and a lot more interesting…)
Wickedness is so much better at marketing…
I think you can arrive at the same idea by appealing to things like “balance” or “harmony”. Courage is a virtue iff it is in balance with the other virtues (the complete cataloging of which, I agree, is unnecessary).
Yeah, McCloskey spoke in terms of balance. When I read Bourgeois Virtues I wasn’t familiar with the concept of the unity of virtues at all so I thought of it in a vaguely paretoish optimization terms. Whereas I now don’t think that’s quite right (not that I’m accusing McCloskey of saying it is; it was my ignorance not her ideas that lead me to that reading).