It's easier to sing the vowels if you flatten them. Their accent doesn't become American, it just becomes flat - and that's not even all the time. I think you ought to listen to more British singers.
If there is any advantage to the American accent, it would be that it acts as the "text to speech" or "robot" of the English language: It pronounces every syllable cleanly, by the text-book rules, and omitting un-needed vowels from the written language. It's clean English, but with absolutely no character (well, then there are regional accents like in the South... that has character...). The Canadian Accent is also quite close to English, with a few notable differences.
My order of accent preference I would put
- British
- Scottish & Welsh
- Irish
- American/Canadian
- Australian (sorry :[ )