To be clear, I'd wager that (at least) 95% of the time good-quality structural 4x4 posts are fine for most hammock applications; I hang off 4x4 posts regularly at home, strung between my front porcch and either a tree or another 4x4 holding up my daughter's playhouse/swing set. However, they are natural products, and like all natural products, individual units can exhibit structural variation that takes them outside of the safety limits of our expected use.
That said, just as we include substantial safety factors (typically 5:1) for hammock suspensions, 4x6 and 6x6 posts probably aren't overkill for anyone who decides to use them, especially when planing for contingencies like tandem hanging between the same two posts. They are just a prudent option that keeps you covered under virtually all "what if" scenarios.
In the case of a square pergola made from 4x4s -- much like my front porch -- those horizontal cross-braces dramatically increase the strength and stability of a 4x4 post bearing loads along the vectors typically associated with hammock applications, and I wouldn't have any qualms about such structures under typical kinds of use.
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