Burgundy's a great choice and just makes your white shirt/darksuit pop with color.
I think it's more of there is always something which would look better. Though I suppose there are more factors at play than merely looking better when choosing clothes. If you've worn light blue shirts 3 days in a row, perhaps you'd want to go white just for the sake of variety, even if it doesn't look as good.
What's not to like really? I like white shirts as well there's no analyzing involved for white shirts you can wear it with anything.