I'm glad I found someone that feels that same way. I used to walk by a BdB on my way to work and I couldn't help but notice the horribly stereotypical cartoon they use as their mascot.[0] My thought experiment for this image is: Imagine how this type of caricature looks like for pretty much any other genre of restaurant (Chinese food, sushi, burritos, etc). It's probably super offensive. To me, that's a good indicator that this caricature is offensive too.
I think Italian-Americans see "cultural appropriation", caricature, non-Italians portraying Italians in movies, etc as part of the process of integration.
If someone with no Italian heritage wants to open up a pizza shop or sell pasta and put a big statue of Mario in front, go right ahead! If it's good, we'll eat there.
You know who made the best pizzelles in my family - by far? My mom's Irish-German stepfather.
[0] https://media-cdn.tripadvisor.com/media/photo-s/06/d7/fd/30/...