Three significant problems with the claimed links between consumption of meats, processed (whatever that means) or not and health issues are:
1. Confounding factors - ie: don't blame the steak for what the cigarettes, beer, and potato chips did. While study authors may claim to adjust for such factors, it's essentially impossible to do so correctly. How do you how to adjust and by what amount? Based on other (flawed) studies?
2. You can't do "real" experiments here like you can in physics, chemistry, etc. It's nearly all observational studies. And really bad ones at that. Typical are the food survey questionnaires. Ask a group of people to think back (or log) and report how much of such and such types of foods they ate over a 5, 10 or 20 year period. No, don't laugh. They actually do this. And then use the data to write papers. That get published. In cases where some sort of pseudo-controlled experiment is performed (feed N subjects substance X and measure some body response), N is often surprisingly small. This allows for the fun game of running a bunch of such experiments, and cherry pick the one with the results you wanted. The rest get memory holed.
3. The claimed risk factors (17% greater risk of dying from eating two eggs a day!) appear large, but in reality are quite small compared to associations we know are real, smoking and lung cancer being perhaps the gold standard here. Physicists and other hard science folks routinely laugh at medical study results, and for good reason. The p values from nutrition/etc. studies are so abysmal that not only would similar results in a physics experiment not get you published, you'd probably be laughed out of the the room for even suggesting it.
Consumption of meat has, if anything, been on a decline, especially red meat. What has also been on a decline is home-prepared meals. What has been on an increase is pre-prepared convenience foods, which is evident by glancing in the carts of your fellow shoppers at the supermarket, not to mention the shelf space at the store. Virtually the entire typical supermarket now is prepared foods. Quick and easy which leads to more consumption (as MDK2 pointed out is certainly a major factor). And a HUGE profit center for store and manufacturer. You can turn pennies of potatoes into a bag of chips. That sells, per pound, for more than chicken. Follow the money is certainly as true today as ever. No need for any conspiracy theories either, it's just all the interested parties do what is in their best interest, though perhaps not yours.
As with Lex, I eat an animal centric diet, and have for 22+ years now - shifting slowly over that time to almost but not quite exclusively animal based after first starting with just cutting out the obvious crap sugar and starches (cookies, bread, pizza, rice, pasta, etc.) I've documented my maintained 100+ pound weight loss elsewhere so I won't go into that here. My diet is essentially meat (mostly beef and chicken, pork, and rarely lamb (which I love but it's insanely expensive)), cheese (cheddars are my favorite with smoked gouda a close second), and eggs. I do occasionally add mushrooms, and somewhat rarely small amounts of onion/tomato for flavor. I just made a big batch of meatballs, there's some minimal tomato sauce coating them, I also melt an 8 oz block of shredded cheese on top.
Nearly zero fiber. Not only did I not find any beneficial effect (as Lex noted) I found a negative effect of fiber consumption. Others with a similar diet have reported this. There's some conjecture that fiber is only necessary if you're eating a high starch/etc. diet.
I've made my own deli style meats in the past, it's a bit of a pain, but not terrible, and I have an electric meat slicer, which considering the insane prices of sueprmarket deli meat quickly pays for itself. I have found a few supermarket brands that are not terrible, they do have more salt than I'd like (from a taste POV, my blood pressure runs 105/60 or so, so that's not a health issue) so I don't eat them that often. Sometimes I'll take deli ham and put it in a pot of warm water on the stove for a few minutes to both warm it up and remove some of the salt. Then throw it on a plate, put sliced swiss onto top, and melt that. Ham & cheese "sandwich" on a plate. I do similar things with cheesesteaks and hoagies - I think you midwesterners use the term "sub"

What I don't think is (or should be) controversial is that the proliferation of what is called "junk food" by all sides of the nutrition debate, as well as the normalization of the result, is taking a huge toll on society, both in terms of health and medical costs. How many steaks or salads people should eat should be waaaay in the margins of the debate. But, again... follow the money. Also, Big Pharma(R) cannot be too displeased with the results of SAD (Standard American Diet), either.