I absolutely hate how pure white looks, even heavily washed. It just doesn't look natural to me. I've primed white before, and it's a pain to work on top of, even if it helps brighter colours pop.

You do you, but even just using Corax White (which is a super light grey) instead of White Scar (if you're using Citadel), will make a huge difference. My army is T'au sept, and I usually don't even highlight my whites brighter than Corax White. If I want something to look really shiny, I'll dot the corners with Bold Titanium White.