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If the useful commits are the "baby" in your bathwater analogy, all the useful information in those commits is in the squashed commit.

This assumes a branch being merged in represents one logical change (a feature/bugfix/etc) that is "right sized" to be represented by one commit.

Yes, but now it's mixed with the bathwater, and now morph into another metaphor as it become the needle in the haystack.

It's okay to have 'low information' commits one can easily ignore in your history, as long as the 'high information' ones stay readable and coherent.