For about ten years I worked for composition shops, and eventually for a maker of typesetting systems. Through blurred eyes I could tell TNR from Baskerville from Garamond from Janson from ... Some of these fonts I can still identify.

But I have no idea what font was used in the book I just finished reading or the book that I'm returning to later today. My main question about a font is whether I can read it with old eyes.

I do agree that designers should care about these matters. I'll add that for some portion of the reading public TNR more likely means The New Republic than Times New Roman.

[Five minutes later: the book just finished, What We Can Know by Ian McEwan, appears to be set in Palatino, never a favorite of mine. The one I'm returning to, I'm not sure.]