OK, I won't retype everything I said before, but as to budget:
If I plan very well, and make everything from scratch, I can manage to keep the budget around the same as when we relied on grains. But it's even easier to blow the budget eating this way when you maybe have invested a lot into good meat, dairy, and produce and then have a week or month or whatever where you ALSO go get more convenience foods (especially if those prepared foods are a decent quality, you know?)
That can probably be said about any diet, but there you have it. I do buy corn tortillas and serve the occasional rice, chebe, and pasta. (Maybe once a month for each?) This helps the budget, makes my family very happy and keeps everyone from complaining about food too much. lol
Another thing that helps both with budget and weight control for me is to really fill up the meal plan with the good foods (that are lower cost) that I WANT to make sure we eat. Eggs and raw milk come to mind. If I make sure we are getting enough nutrient dense fat and protein from lower cost sources it helps avoid splurging on costlier things.
And yes, I do consider my farm eggs ($4 a dozen) and raw milk (7.50 a gallon) to be lower cost when you think about the cost per serving.