To me, there's a lot of value in playing openings where you're throwing yourself on your own devices, and forcing yourself to be creative.
But you can do that in the context of the Italian game. You don't need to play bad moves (like 1.a4) to accomplish it.
That being said, I remember an internet post from a guy who lost a lot of games to someone who opened (as black) 1.e4 a5?! 2.Nf3 Ra6? 3.Bxa6 Nxa6
The point being that the player of the white pieces didn't seem to understand the resulting position (being up an exchange, but not knowing how to create open files for his rooks to take advantage of it - while also really needing his KB to attack with).
I wouldn't recommend such a thing, but the point is that the player of the black pieces had said, "Here's a way I can play for a quick win giving up less than it looks like I'm giving up, let me see how he handles it" and then playing very creatively.
(An exchange is not a lot to give up - particularly in the opening when the advantages of the extra rook are going to be hard to demonstrate).
But, as I said, you don't need to play 1.a4 to adopt that mindset.
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