In my experience, keeping fat down to reasonable limits is most effective for losing bodyfat. You very rarely see high-fat cutting diets employed by successful bodybuilders for this reason. There's an upswing in keto diets, but many of them admit that they're more catabolic. Most of theirs are actually almost non-fat, which is less than ideal health-wise as we all know, but still effective for losing fat. If you eat carbs in a glycogen-depleted state, it gets stored as glycogen. If you eat protein within your synthesis limits, it gets turned into various structures, enzymes, etc. If you eat a bunch of fat, it gets packaged into chylomicrons and sent to the fat cells for the most part if you are eating the amounts than many high fat diet proponents are advocating. If that results in ad libitum hypocaloric eating all told, then it's effective. That simply doesn't work for me.
Eating a high fat diet is best for health, but not always best for weight loss unless you can glean a ton of satiety (and thus are eating fewer calories) out of it, which usually requires little to no carbs. If you don't want to go that route and you want to lose bodyfat, then you need to keep an eye on the highly energy dense fat that you're eating. Eating fatty meats is a lot different than downing as much butter and coconut oil as you can stomach.
Eating like a contemporary hunter-gatherer or an anatomically modern human from the past is great if you have the same lifestyle and goals as they do. Odds are you spend most of your time around 70 degrees Fahrenheit and are markedly less active in general than they are. We can try to simulate the feeling of really needing to survive but it's simply not the same.
A guy in the pleistocene constantly working hard to not die simply has different goals than an office worker in 2011 trying to get in shape for summer.
That all being said, if you're at a desired body fat percentage that you are maintaining with a really high fat diet, then go for it; it's likely a lot healthier than shifting that to excessive protein or carbs. I dunno how many of us are actually in that situation though.
I would never advocate the ridiculous practices of eating only egg whites or "boneless, skinless chicken breasts" but let's say you are eating high fat paleo + starch and you hit a plateau. Your breakfasts are eggs, bacon, and potatoes lunch is fatty meat and veggies or starch and dinner is similar. Let's say carbs add up to a reasonable 150g a day. You might be tempted to start cutting the carbs back, but maybe the problem isn't that you added carbs, but actually that you've made 500 calories of butter disappear into those potatoes and other vegetables. This is what I was doing. As you increase carbs, you are increasing fat intake substantially. Now, if you kept the diet the same but just ate steamed sweet potatoes without butter or rice, you'd be cutting a lot of calories out of your diet without losing out on much in the way of nutrition. Your carbs are still appropriate and your performance doesn't suffer as a result, but you've pulled out some additional fat padding on your diet that was holding back a body fat loss. "Fat doesn't make you fat" is simply not true. Converting amino acids or glucose into fat is far less efficient than simply converting fatty acids into triglycerides. Evolution will favor the more efficient process. If fat comes packaged with meat, I say it's fine, though an all bacon diet would likely be less than ideal for fat loss. Cutting back on neolithic saturated fat in some instances can be highly effective for breaking through a plateau.
The same would be true for switching to slightly leaner cuts or trimming obvious huge gobs of fat off of your steaks temporarily. You still end up eating a lot of healthy fat, but you're controlling the energy density of your meals to a greater extent. Once you get to where you'd like to be, you adjust fat intake upward until a balance is reached.
For example, I was eating tons of lamb blade steaks that were strikingly fatty. I switched to leg steaks, and even though there's more meat on the latter and I'm obviously sucking the marrow out of the bone, I'm sure the caloric difference is in the hundreds for a day. I am constantly thinking "how many hours did I just get out of that meal" in terms of satiety, and it ends up being the same. The fat simply isn't conferring the advertised level of satiety.