First thing first, eating only meat is not as bonkers as it might seem. In fact, it's a huge an distinctive part of the Dukan diet, which starts by imposing a protein-only diet(§) for, guess what, ten days to two weeks. This is to get the same effect that Sonya Mann (the author of the article) experienced and thus to give a confidence boost to the dieter as immediate result help the dieter to go through the diet (keeping dieting is the hardest part of a diet as anyone that has dieted at least once can tell you).
After that you integrate vegetables (in this phase you're still losing weight) and go on like this with meat + vegetables for ideally one week for each kilogram you want to lose.
After that, you can basically start eating regularly(§§) for the rest of your life BUT you must always observe the meat/protein only Thursday (§§§), this also for the rest of your life.
I have followed the Dukan diet and it affected me positively and I have lost a significant amount of weight (but keep in mind, I was/am mildly overweight -- that is, i have belly fat).
The book that Dr. Dukan wrote about its diet is very cool because it explains in simple but proper terms how the diet works and why it works. It also explains what to expect and when to expect sub-optimal results (for example, women should expect a wider variance in results because of hormonal ups and down -- mostly due to menstrual cycle).
So...
Going back to the story, eating meat only can be sustainable. Not sure how long, though.
Surely, I don't think it's such a great living. What bothers me the most, actually, is that the meat you buy nowadays at grocery store is filled with hormones and antibiotics (used to get animals to grow very much and very fast). One could argue, the humankind has evolved to eat meat, but also to go hunt for meat and eat it "fresh" (as in non-conserved, with no preservatives, no hormones and no antibiotics) but that's unfeasible nowadays.
Notes:
-----
(§) calories only, plus yoghurt and integral oats to help with digestion.
(§§) regularly as in european-regular
(§§§) Thursday has been chosen randomly, for no particular reason, it's just a convention.
Edit: formatting.