> but would still strongly prefer over one-or-more other candidates?
In fact, this is why I argue for STAR or score. It encodes information for better than a ranked (ordinal) system. In any ranked system you encode your preference with equidistant from one another. Where as when you score you can indicate a much stronger preference.
Here's an example. Let's say I REALLY like candidate A, moderately like candidate B, and strongly dislike candidate C.
Ranked:
A > B > C (with my encoding I'm saying that my preference of A over B is the same as my preference of B over C)
Scoring
A: 10, B: 7, C:0 (with this encoding I can indicate that my preference of A over B is not as large as my preference of B over C. Obviously we are capturing more information here)
Let's just encode information better, I agree. But also let's consider other factors like how easy it is to count the votes (which every cardinal system is going to beat ranked systems).
[0] That same preference where the distance between STAR, Score, and Approval is smaller than the distance between preference of Approval over IRV (e.g. STAR: 10, Score: 8, Approval: 7, IRV: 3, Plurality: 0).