I don't usually go negative here, but
1. I was an English major,
2. I was a copy editor, and
3. I read The Book of the Courtier in the course of my studies.
So I winced a bit when I read "Natural Sprezz" by the generally very smart guys at Put This On, itself probably the most widely followed #menswear blog around. Sprezzatura gets used a lot in describing menswear, but when Baldassare Castiglione coined the term, it basically meant apparently (but affectedly) effortless nonchalance. That is, going to great lengths to appear not to have gone to great lengths. You see this every World Cup from the Italian team coaches--they tend to, say, tie their neckties so that the narrower blade hangs several inches below the wider blade. We are to believe that this was accidentally done for international television. So sprezzatura is a squishy concept, difficult to measure because measuring fixes it in spacetime.
Wearing a linen suit is not, as PTO has it, sprezzatura. You cannot wear a linen suit in a way that makes it seem like you put on a linen suit by accident, especially in the summer. Linen suits are nonchalant and effortless, but there is an element of irony in the use of sprezzatura. Wearing a linen suit on purpose because it's effortless and nonchalant is a great idea, but anything worn in earnest is not sprezzatura.
Likewise, Beau Brummell's extraordinary attention to the tying of his cravat was not sprezzatura. Sprezzatura is like Fight Club: rules #1 and #2 are that if you are talking about it, you are doing it wrong. Sprezzatura is futzing with your pocket square for five minutes (or hours), when you are alone, to get it to look like you just grabbed it off the shelf and stuffed it into your breast pocket without thinking.
Sprezzatura is a fun, precise word! Let's keep it that way.