IMHO if your body has reserves and your metabolism allows you to quickly and effectively convert those reserves, primarily fat, into usable energy, you could indeed operate for a time on just vitamins, minerals and water.

But most people could do just about as well without the vitamins and minerals for some time at decreasing levels of output and efficiency. In theory the vitamins and minerals hold off the deterioration for some amount of time.

Most Americans have ten to twenty pounds of fat reserves. The problem crops up that not everyone is gifted with a metabolism that can operate on fat reserves as the primary energy source. Many people need some amount of external caloric input over and above vitamins and minerals. Some percentage, serious hypoglycemics and diabetics as a start, could easily die trying to operate from internal fat alone as a calorie source.

My estimation is that Life caps are mostly vitamins and minerals. If your metabolism is forgiving and you have reserves you might be able to go a week or so on them. But you might do about as well with regular high-dose vitamins and eating worms. I doubt you would feel fed. Get used to that stomach on backbone feeling. And after a few weeks they may have to use a apple corer on you to open you back up.

Survival Tabs look to be the descendant of the concentrated survival foods that were being researched in WW2. They have vitamins and minerals but also have a considerable amount of actual food. The daily ration of twelve rather large horse tablets has more bulk and weigh but in return you get something a bit closer to a starvation ration that has been heavily fortified. You might go a few weeks or a month on these without too much trouble. I suspect your going to feel empty and hungry much of the time but the feet would keep moving and your bowels too after some time.

Moving up to almost real food consider something like Mainstay survival bars. They are compact but bulkier and heavier than either of the two previous products. But in return you get a fuller allocation of calories, a better chance people with less than perfect metabolisms can run off it, and the ability to run on this one source longer without discomfort or hazard.

Of course the long-term solution is real food. But real food can be a pain. It is heavy, bulky, doesn't always store well, and it often needs processing and/or cooking.

Everything is a trade-off.