No.
Commercial printing most commonly uses 150LPI line screens so 300ppi at actual printed size is all that’s needed.
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I meant that there must be a setting in Illustrator to select the number of dots-per-inch that Illustrator will rasterize to (that is, to change the number 1/72" that you stated).
Yes, it can. Here is a 0.25" circle, and the same circle rasterized at 5 dpi.
(jpeg enlarged 3x for clarity)
Yes, when I mentioned resolution 10x that, I was thinking of the resolution that’s used internally in some print processes, but that is downstream of desktop software. In those processes the resolution produced by desktop software is lower, like you mention.
(I found an article from 2012, about the downstream process steps, that called 2540 dpi “low resolution”! 
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