If this is about the recent birthday video... well, tbh, I think we would sing in a same cutesy way. I don't know anyone who is going full broadway or at least takes this song very seriously.
About other songs.. I can't imagine a song like for example HONEY to be sung in a serious tone. Neither STEP you.
It has this whole 'giggle giggle falling in love' aura about it, so singing it in a cutesy voice seems... a good fit?
As for a songs like Depend on you or poker face, I think I agree with Chris85 that she is trying to sound close to her sound in her earlier carreer. But then again, these two song sound also very upbeat. She doesn't sing YOU like that, so maybe it is just fitting the tone, or uplifting atmosphere, of the song.
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