Sure, but you don't get the variety. If you move out to rural France but are used to rotating among eating Mexican, Japanese, Chinese, Spanish, Thai, etc. throughout the month, you might be disappointed with the lack of choices.
You are probably used to this rotation just because you grew up in the US. As someone who has grown up in Italy we don't think about food this way, not even regionally. I.e. don't expect a great risotto in Naples or a decent carbonara in Milan...
I think there is a spectrum, the US being a country of immigrants is on one extreme, Italy having been several different independent states up to 160 years ago and having many different climates and cultures is on the other. While it's true that the Italian approach to cuisine might be overly provincial I think that most of the world is closer to Italy than the US.
Being in rural France, I like trying some new foreign cuisine once in while as much as anybody else, but it wouldn't come to my mind to make it my daily routine.
Going out of your way to not eat local stuff is completely pointless to me. People take quite a lot of pride in having good stuff specific to their area.