What's the hierarchy that it establishes that the large type, all-caps, and oddly-spaced embossed icon didn't already establish?

I guess it's not really the "flourish". (I like that term for it)

What really bothers me is that, on the whole, it feels like the designer put more effort into the flourish than into creating a design that would support and enhance the communication of the content.

It's the (wrong) idea that you can appropriate these stylistic elements that will make a design appear current, cool, or 'with it' - and that somehow adding in what all the old-timers would call "bells and whistles" is a worthy trade-off for the practice of good design.

Agreed. But I don't know what visual hierarchy means.