I personally like the look of no back splash but does it make the kitchen look unfinished?
FYI - not sure how to fix the second image :)

If you like the look, then *looks wise* I'd say it's fine. But what about practicality? Are you concerned about food splatter behind your range? or water spills from the sink?

I personally think a well done back splash looks fantastic, but looks aside, they certainly serve a purpose.

I love a backsplash and think one would look great in your kitchen. Plus, water/grease spots are easily removed, whereas a painted wall can look gross after a while. Lovely kitchen layout, by the way!

I forgot to say tell you the kitchen looks great!!!

We have rules in Australia for wet areas and stoves.

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This is a hard one. I am a big proponent of backsplashes, both for adding interest and for practical purposes. But I love the clean look of your walls now and I love the color. If you do a backsplash you will need to decide how high to go in each area. That is not an easy thing to do. Hard choices I agree.

Sure it's better to have a backsplash in the wet and cooking areas of the kithen. If you don't like it [what I really understand] it's possible to paint and /or wall paper these areas like the rest of the walls and then add a thick glass in order to get the protective effect.
I love it : I find it gives a great decorative and modern look to a kitchen.

No backsplash except behind stove, but I'm not sloppy when I cook. I've always had paint or wallpaper which are much, much easier to change than tile when redecorating for a fresh new look.