Cary Grant always sounded like Cary Grant, which was never anything less than perfect for whatever part he played. Kenneth Branaugh's "American" accent was highly distracting--

I am a good mimic, which has been a problem for me, because it made it easy to do impressions rather than to find my own voice. I used to do a lot of Balkan stuff, but singing songs in languages that I could not speak ended up being more like doing parlor tricks than like really singing.

Though I it isn't strictly accurate to call it a "Chicago Accent", the point that certain singers tend heavily toward doing a "blues impression" is valid. In some cases, the affection is so transparent that it is embarrassing--a lot of people do make it work, though--