DAM is a tool designed to be specifically good at managing digital assets (that is, doing one thing well), hence the UNIX-y comment, but I can see why you’re saying directories are UNIX-y as well. Many newspapers use DAMs or custom CMSs with DAM features (eg, NYT’s Scoop).
I wouldn’t. I’d keep them separate and if the DAM has CDN integration (eg, delivers images directly or maybe pushes to an S3 bucket or whatever), I’d just build shortcodes around whatever the URL conventions are.
Like I said above, I think there are great use cases for generators like Hugo (obviously, it’s my favorite FOSS of all time), and agree with @bep’s metrics for certain, but @budparr is talking about best practices and recommendations. If your client has a lot of valuable image assets, I would be loathe to recommend directories. I also think these decisions are less about tech and more about internal resources and alignment, especially when you have to wear many hats like Bud does (e.g. dev, design, content strategy, editor, etc). You could have everyone using a really strict set of standards and naming conventions, but I’ve never seen that work in the real world with more than 1 or 2 authors (think company shared drives, which IME are a real nightmare).
Sorry I can’t contribute, but I don’t have many well-informed thoughts on WordPress in 2018