I love my white shirts! I used to "save" them for wearing to work, but them I took ANgie's advice about duplicating items that create laundry bottlenecks. Now I can easily wear a white shirt layered under a sweater with jeans on a Saturday, or tucked into a full skirt for church, and I feel so much more like "me" this way.
I too find the white collar really useful in providing the brightness or contrast I need next to my face--it makes muddy mid-tones like grey go from blah to chic.
Like Marlene, I never look "polished" even in a white shirt, so I don't even try. In fact the day I discovered my RATEness was after giving a talk wearing a white shirt with a blazer (rare for me), I spilled tea on my shirt cuff and rinsed it and rolled both cuffs above the blazer sleeves and all of a sudden something clicked in place.
Re: the ironing: if you shake your shirt out really well as soon as it's done washing, and hang it to dry immediately (ideally, in a bit of wind), you may get away without ironing.