I find the integrity graph minimally useful, but only because the colored boxes already give much of the same info. I do activate it sometimes for a clearer comparison, and I know players who use it as their primary graph.
It's the only graph I use! I've learned all my coverage values and I wouldn't even be able to tell you what the other graphs display. I need the precise health values to determine which item to replace when I come across a new one.
And that is what I'm talking about. If you have played the game a lot
and know the coverages by heart (and have the right mind for that exercise) you are basically doing the vulnerability check yourself. If the equipment you are deciding on is all similar in coverage and total integrity, the relative integrity view can tell you at a glance which item is closer to breaking. The vulnerability view would work the same way (the way I described it, it's more like 'safety' - higher values are better).
The view I'm suggesting would essentially tell someone who doesn't know everything already, "which equipment of mine is likely to break first, and which will last the longest?" This could guide decisions about which way to swing your build when you have options. Besides, just like the current integrity view, it could let you see at a glance what to replace. For two parts with similar coverage values it would read essentially the same as the current integrity view.
One possible problem is that if certain items have a high integrity and very low relative coverage, they might squish the other values too much, but in that case I could use the longer method and puzzle it out via integrity and coverage views or item descriptions.
Like others I almost exclusively use the 'q' info (usually what it sits on for me also) and integrity views, occasionally glancing at coverage if it's necessary or I'm curious.
I do think the relative integrity is the most useful graph, usually (being the only one that shows changing information). Part HP bars basically. Coverage is a close second. The tactical HUD largely takes care of the other graph's duties in practice, but it's nice to have them sometimes.
So I'd be happy with just the "safety" graph. Absolute integrity is factored into it in a useful (possibly more normalized) way so there's no need to change other views. To be fair it doesn't include effects of shields and such but I figure that's okay, those items demand special consideration anyway.