It's very clear to me that Giovinco could still be a good player on a Lazio/Fiorentina/Roma/Milan/Inter type team.
Heck, he'd probably even be a good player on a good EPL team (Liverpool for example). I have little doubt he could excel in a league with paltry defending such as the EPL, La Liga, or Bundesliga. Serie A just makes things difficult, especially when your coach makes you hold up play for the midfielders when you're 5 foot 5. Heck the MLS is basically EPL style defending, and while it is better, Giovinco looks like Messi in the MLS. I'm sure he'd look pretty solid in the EPL. That's not to say he'd be starting 11 on a Chelsea. Liverpool, yes... What I'm saying: He could probably start on teams that are one place removed from the elite: ie: Liverpool, Roma, Dortmund, Monaco, Tottenham, Valencia, Sevilla, Wolfsburg.
He couldn't start on: Manchester City, United (only by virtue of their attack heavy roster, Ogbonna would probably start for them), Bayern, Chelsea, PSG, Atletico, Barcelona, Real Madrid, etc.
I'm tempted to say he could start on Arsenal.
Here's an interesting way to think about things. He was a sub on the Champions League Runnerup, meaning he is at least in the conversation with players like Chicharito.