That's one of those damned good questions.

I have thoughts, but I'd really like to see some solid information on how prevalent they were, what their previous rationale was, and what accounts for their decline.

On contemporary houses, if shutters exist at all, they're all but entirely decorative. Frequently they're on the inside of a house.

In hurricane-prone regions, shutters seem as if they'd make more sense than repeatedly boarding-up and unboarding windows.

Note that in the case of wildfire, embers entering into attic and crawlspace areas is a larger threat than direct radiant-heat compromise of windows, though ignition of interior furnishings (especially curtains or blinds) by radiant heat does occur. Still, window and other structure penetration shutters seem as if they'd be a potentially useful addition.