It's not enough for me, but then that's my problem. So, compare the following:

1a. rubber baby-buggy bumpers
1b. adj - noun - noun - noun
2a. American rock star shenanigans
2b. adj - noun - noun - noun

In (1a) rubber modifies bumpers, but in (2a) American modifies rock star. Why? How? Will hyphens help? I think the use or abuse of hypens is as idiomatic as nominal compounds.

Let's just drop it, and agree to disagree.