So let me give you my overview/explanation of the general reasons why occasional fasting is a good idea (I didn't read the site mentioned in this post so I am not sure if anything was mentioned there too).
You are basically trying to reach a balance between multiple goals:
-getting high quality nutrients in sufficient amounts
-maintaining proper levels of hormons, appetite, energy balance
-recovering, detoxing and giving rest to various systems in your body
Because of this, you are already alternating between intaking food and decently long periods of fasting (usually the 8-12 hours between dinner and breakfast while you sleep).
A worthwhile note...my personal diet consists of a large portion of cottage cheese (slow-digesting casein proteins) with a good dose of fiber, and a colon cleanser that has the effect of slowing digestion. This leaves me with a long-lasting, slow-digesting source of protein and fiber, that keeps me fed throughout the night. No 8-hour period of fasting.
I do that too actually (I use pure casein proteins and sometimes normal fat-free or 2% cheese, I personally can't stand cottage cheese taste and consistency). It's a very good idea especially if you are working on building muscle and recovering.
But the point that I was making is that most people do have more or less those 8 hours of fasting.
The idea again is not that eating well with frequent meals is bad, not at all, that is good too. It's just that occasional fasting has also many advantages that you would be missing out on if you did that routine continuously without ever alternating anything else in between.
Let's consider the extremes first, will something terrible happen if you just drink something like water or tea for those extra 12 additional hours? No. You're not going to explode or anything. Similarly would you be better off being able to eat continuously even through the night? Not really, that goes against giving a rest to your digestive system. You are basically sacrificing one goal to try to max out a bit more another, like gaining weight as fast as possible even at the cost of feeling stuffed all the times.
why should you give your digestive system a rest? I never have before (intentionally), and my digestive system works great (except yogurt gives me gas....lol).
Again I would say you don't -need- to give your digestive system a break, but it can be beneficial to do it. Just think of it as some other things that are nice to do occasionally, like say a sauna or a massage or rotating in a different exercise program or even a few extra days of rest away from exercise etc.
Don't get me wrong, your digestive system could be working perfectly well without ever fasting especially if you are eating perfectly. On the other hand it's also possible that it might get a bit out of whack despite your best intentions, and in those cases something like a brief fast can make it easier to recover.
It's a bit like in training, where you could accidentally overtrain and not realize it, so rotating in a few extra days of rest tends to be very useful in general and even more so when you are potentially overtrained.
In reality, there are several mechanisms occurring during fasting that help you stabilize hormones and appetite, and continuous eating to extremes actually destabilizes them more. Your body tends to adapt to continuous signals and ignore them or require higher and higher levels to receive a response. Appetite can get messed up by having your stomach always stretched, so giving it an occasional longer break can really help you feel full sooner in response to food, or enjoy your food more while consuming smaller amounts.
My stomach is never stretched. Constantly eating, and averaging <2000 cal. per day means I'm rarely eating more than the volume of a piece of fruit or half a sandwich at a time. More than that and I would feel totally stuffed. My friends look at me weird when I eat at their place, and only take tiny ass servings and claim to be stuffed...lol
Well again that's a sign everything is working fairly well with your diet and you already got used to smaller portions just from your diet and caloric restriction. It can however be a problem for other people who don't currently have a good diet, and an occasional fasting can be easier to try and get that effect for those who are still trying to work on figuring out their ideal diet.
Again in my view it's sort of a quick occasional catch-up and self-check solution that can make you realize if you have problems and help you resolve them (lack of appetite, too much appetite, digestive problems, metabolic problems etc).
You are also more responsive to hormones of all kinds (including those associated to energy balance) if you take occasional cyclic breaks (you even do that for anabolic hormones, and occasional fasting does that for things like insulin).
Interesting idea, and the first thing that's made me consider an occasional fast...I get more drunk if I only drink once every couple weeks...I get more loopy if I only smoke once in a great while...Would I be more energetic after eating if I deprived my body of food for a period first? Still sounds dangerous...
Being energetic is a funny thing, the morbidly obese guy eating 5000 calories on his couch is not feeling very energetic despite having more calories than he could possibly need. On the other hand the skinny mouse (or person) that is fed a bit less food than they need is generally hyper and full of energy. It sort of makes sense if you think of it in terms of evolution and long-term survival, if you are hungry you need to be full of energy and hyper to find food (at least for the first 2-3 weeks), and if you are overfed you can instead relax for a while.
If you feel low-energy from just doing something for 24hrs, that's not usually a real reflection of the energy available to you, just that somehow your metabolism is not quite switching properly yet.
Basically you really don't deprive yourself in the real sense of the word by just doing one day of no food, you just temporarily switch gears, and it's really in no way dangerous for normal people (if you were in the wild again this would be a fairly common occurrence).
In general, even on much longer fasts (which are not what I am recommending in general) people might actually feel a bit off on the first 1-3 days and after that they feel again full of energy (and also find themselves really enjoying TV channels like the food network a lot more

).
In general what I think you'll probably experience if you tried this would be possibly better appetite and enjoyment of food and more energy, rather than less. You don't have to include it in your diet but it can definitely be a good idea to rotate it in occasionally as I mentioned as a self-check and normalizing rest day.