Doing crossfit on hard-core paleo would be tough. I think most of those guys are "primal" not paleo, meaning they ingest small amounts of tuber-type carbs (i.e., potatoes). Ketones are great, but glucose really helps with the high intensity stuff.
Again, that sounds like primal, but the distinction is pretty minimal.
Most modified versions don't last long. If you're still ingesting carbs/glucose, you kinda get stuck in "no man's" land where you're not getting enough glucose to function at 100%, but not yet adapted to burning fat, so you feel sluggish, tired, headachey, terrible. Not pushing you one way or the other, but you really have to commit to it to feel the benefits, whatever they may be.
Well I see as problems, 1, sacrofication of the starches, 2, isomerization of the hops and 3. last but more important, sanitation of the wort. I suppose DMS also could be a problem, but I'm not exactly sure how it is formed. Does it require heat to make (say 140F) and then get driven off at a boil?
Anyhow, yes #2 would require a boil to get good bittering out of the hops, although some will come out with a soak at room temp. The isomerization is iirc a change of the AA shape so it is more water soluable. But it might be only 1/10th ro even 1/100th as soluable, hence why I suggested using a different bittering agent.
#1 I don't think can be done without hitting the activation energies of the emzynes which are in the 140 to 160F range (depending on emzyme).
#3, is clearly the most difficult - how to make it all sanitary.
That assumes pigs, cows, etc eat corn. The missing equation here is grass. Humans can't eat grass, but cows can. They turn hardy, perennial, abundant, prolific grass into high-quality sustaining food.
When I earlier said that I don't use gelatin, because a product from a cow, I didn't mean to imply that I am vegan or vegetarian, as I am not.
I'm more between paleo/primal, and I eat grass fed beef, venison, and lamb along with fish I've got. But I don't want my beer to not be vegetarian friendly, as I would think that my vegetarian friends would not expect to find animal products in my beer!
The thing with me is funny- I'm mostly paleo/primal, except for my beer! I'm NOT giving up my beloved beer. That is the only grain I consume- the grain in my beer. I eat a few potatoes in the fall, but otherwise no rice, wheat, barley, or other starchy foods unless I'm out with friends and then I suck it up and eat whatever they are having.
I do NOT preach my lifestyle, but sometimes I do say something. As an example, I work with a woman a little younger than me. She's extremely obese and always has Twizzlers, chips, and Mountain Dew on her desk. She's always sick, she's always tired, and she's got health issues like bad teeth, high cholesterol, etc. I don't say a word for the most part. But every once in a while, she will make a snide comment to me like, "Must be nice to be so skinny." Finally, one time, all I did was look at her and say, "You just wouldn't want to do what I do". She laughed then, and agreed. She asked me a couple of times what I eat, because it's foreign to her and she just doesn't understand how I am happy with my choices. I've never ever preached to her, even though her young children are also obese. Because she knows this is unhealthy- she's not stupid. But she doesn't want to make changes, and that's the bottom line, so it's easier to point to me as the "weird, skinny person". I don't point to her as anything.
I'm not into "raw", although I do consume many raw or pickled foods just as part of my mostly vegetable diet. But to make a beer raw food friendly would be tough. I think home malting and kilning at a low temperature is far above my abilities, as well as against my inclination. Mead and wine are raw, but I can't really see how to make a great tasting beer this way.