Well, I doubt very seriously you will find a white roll out sugar cookie. Actually, I don't believe I have ever in my life, seen a white dough cookie. Even if you used filter oil thats clear, clear flavorings, and even clear eggs, I doubt the flour would stay white while baking.
Sugar cookies are tricky....very tricky.
How you want them holding up after baking is the key to HOW they should be baked.
You have to know instinctively how long to bake a sugar cookie based on thickness, viscosity, and whether you are wanting a soft cookie or hard cookie.
Sugar cookies bake the fastest of any other cookie, simply because it's simple. Flour, sugar, oil/butter, vanilla....some people use egg, some don't. There is nothing "extra" in the dough to warrant a longer baking time.
Sugar cookie dough is also temperamental while baking. If you don't do it JUST RIGHT, you will never get the cookie you are looking for.
I have to say though.......my granny made the perfect sugar cookie. Firm, but not hard, tasty without being floury, and tasted good with or without frosting. I also have to admit, even through my years of baking, I've only been able to turn out ONE batch of sugar cookies just like my grannies.
But through all the trials, tribulations, and burned batches, I learned that THE trick to sugar cookies is HOW they are baked.
And for the type of sugar cookie I like, how thick I like it, and how I like it to hold up when I eat it.....I bake mine for EXACTLY 7 minutes on 350. They may not be like that one perfect batch I made like granny used to, but they are sure as heck the closest thing to a perfect sugar cookie that I like.
Yes, the dough does have a lot to do with the cookie, but the kind of cookie you want at the end.....well, that's all in how it's baked. And it doesn't matter what recipe you use.