You mentioned it yourself, there is an issue with where power and versatility are not equal at all points:
- Something may be "Strong" power in one or two roles, while only "Average" power in others, and "Complex" versatility.
- Something else may be "Strong" power in all of its roles, and "Complex" versatility.
Are these two the same? I would suggest not, but the system proposed wont handle it.
Indeed, a similar issue crops up with Bard and Psychic Warrior:
- A Bard is "Strong" power in some of its roles (notably those revolving around buffing and bluffing), while only "Average" power in others. It is, however, "Complex" versatility.
- A Psychic Warrior is "Strong" in all of its roles, although it is only "Simple" versatility.
The Bard is either a full tier ahead or not at all, depending on whether you choose "Strong" or "Average" for power.
Another issue that could be highlighted here is that all of the Psychic Warrior's roles are combat-orientated, even if it is not a "One-Trick-Pony", while the Bard has roles in both social and combat situations. Lets suppose the overall number of roles covered by the two were the same/similar, the Bard would still be more versatile in my opinion for having covered both combat and social situations. The proposed system doesn't cover this facet of versatility.
Basically, I don't think a tiering system is that good at covering such a number of variables. Personman's Niche system was/is the best I've seen at truly getting into where the classes are, although it is a little too coarse-grained. This issue is probably best highlighted by looking at the chart for Monk and Barbarian and then noting the final score.