The "block context" for which setting margins is a good layout abstraction is not the technical "block", "inline-block" etc. of CSS, but the general situation of measuring the empty space between homogeneous rectangular blocks.
If you want to place a slider between two text paragraphs, the slider isn't a good match for them (even if rectangular, it's far smaller) and you'll have to give it small or even negative margins under the assumption of the text paragraphs having normal, big enough margins.
And this highlights the issue with the idea that "children would expose their preferred margins, which these layout contexts could take or not take into account": a reusable and modular layout should be bottom-up, with components knowing what CSS rules make them look good and containers respecting them. Since the slider is small it can have smaller margins than the text paragraphs, but a container that knows that its middle child is a slider is a complicated and ad-hoc container.
