The only issue with not adding healthy fat or oil to your diet is this:
When you are physically active (unlike hanging out in a cubicle all day at work) your body will at some point NEED the fat. Otherwise you will start consuming your muscles for needed calories.

Yes, oil does exist naturally in food. It also can go stale then rancid in long term storage. So if you are carrying brown rice or things with flax, wheat germ, etc - be sure to keep tightly sealed. The good thing is normally you can smell it when it goes stale, flat smelling.

As well, for long term hiking don't discount a little oil added to dinner to keep one "regular".

While one doesn't want to go on a fat fest something to consider is the average 20 something thru hiker of the PCT. By the time I see them in mid Washington in late August they all look the same: ultra thin, just wiry thin muscles and they eat all freaking day long. They literally cannot get enough food in by then - and fat tends to a big choice.

You just have to pick wisely what you use for fat and use it sparingly.

Most of all though with an all whole foods diet...don't forget the herbs and spices to make life taste better - and expect longer cooking times - the trade off on cooking time vs fuel would be a big reason to carry precooked versions. Your wood burning stove will remove that issue.

Btw, if you are planning on doing whole grains have you ever read the original green cover version of "Simple Foods For The Pack"? You have to get the 1970's version - it covers cooking lentils, brown rice and other staples.