All this is true, and you have correctly identified her role in the game. However, as the Original Posted noted, it is her skills that don't match this role particularly well, most notably her passive and E passive.
She is a utility champion, so why does she have a pseudo damage modifier with her passive (not unlike Caitlyn's 'Headshot' passive) that only scales with crit? Many people have come up wiht way better ideas for her passive than it is currently on live, and certainly better than anything I can think up on the spot here.
Why does her E passive give her increased gold income to itemize as if she was a hyper carry, when she:
a) can never max that skill because she needs to max her utility
b) doesn't need to rush damage items anyway because she is utility based, and doesn't scale, (in the sense of raw damage, as you noted) and so doesn't have a particular 'power spike' she needs this passive to reach and be relevant (in my mind a better e passive would be something like increasing attack speed on a target she has slowed - kind of like the way jinx's Q works - which would be a skill that would then have more relevance as one she is maxing in the late game, while also not over powering her damage).
Ideally I like Ashe as the utility-centric ADC, that can really bring a high damage team together. I was rather fond of the Ashe blue build (back when it was still viable before the IE and Triforce changes) and even now in spite of it's less effectiveness I still like to build BOTRK, Muramana, Frozen mallet, and sometimes even an Iceborn Gauntlet just because of how well the supplement her utility. I just wish that her skills (Passive and E respectively) better suited/reinforced her meaningful style of game-play.