Why not run all out and rest until you feel enough to do it again?

Because running “as long as you physically can” would do more harm than good, and might even land you in the hospital or kill you.

“What doesn’t kill you makes you stronger.”

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It's very hard to plan your days and weeks around running every 15min or so, eventually eating and sleeping, and then ultimately getting injured.

Running primarily involves two energy systems: aerobic and anaerobic. Long distance running is overwhelmingly the aerobic system, which is your muscles using the oxygen your blood supplies. When you run faster than your blood can supply oxygen, the muscles use another energy system.. the anaerobic system. It works for short bursts of speed, but then it's quickly used up. (Okay, that's oversimplified, but hopefully, it gets the point across.)

In short, running really hard, recovering, and running really hard again is training the wrong energy system. Your distance running won't improve very much. You'll just get better at doing more reps of running fast and then recovering.

Now, for adult recreational runners, there is a third approach: it's called Jeffing or the Run/Walk Method. You run a little faster than your steady state running pace for a set time, say three minutes, and then do a walking recovery of one minute. Beginners who are struggling to run at all might run 30 seconds and then walk for 2 minutes. Gradually, the running portion becomes faster and longer, while the recovery drops to one minute and stays there.

Jeffing is a good way for injured distance runners to get back to their former fitness level after being away from running for several months. The runs portion isn't fast enough to get deep into the anaerobic system and the walk allows the muscles to drop back to the lower range of the aerobic system. It's an aerobic workout, but you're learning to run faster when you are actually running.

However, for younger runners who aren't training to "finish" a marathon, eventually you'll need to start doing some steady state long distance running.

The reason Jeffing works for older runners... say, age 40+ and out of shape... is that their "run" pace of 12-14 minutes/mile or slower isn't really running... it's a shuffle. Over time, they can learn to shuffle faster, but they never actually lift their foot very far off the ground so they haven't learned the range of motion to actually run.

OP, in short, your idea won't work as you described it, but if you read up on Jeffing, it could help you get in shape faster.

You'd end up injured or burnt out/overtrained if you ran to complete exhaustion in every training session. It's completely unnecessary as people improve off steady state/easy running without the additional risk factors. Time has proven over and over again that steady state running or easy running is best for beginners to avoid injury and to get the body used to running after being sedentary for years (usually).

I think that the answers so far have not fully understood what the OP is asking.

I think that ( and I could be wrong, and the one misunderstanding here) is that the OP is asking why do runners run frequently, at most often sub maximal efforts. He’s looking at it through a HIT Arthur Jones / Mike Mentzer lens. I’m guessing that he’s asking why not do a race type effort at your preferred distance (or a range of distances closest to it), go to the well, so to speak, but then take how ever many days off to recover, super compensate and then come back to go again, once recovered and refreshed. Why instead do runners go sub maximally, pretty much day in and day out.

OP please correct me if I’m wrong.

Sounds like a break through training method...

The only thing you need to figure out is how fast to run when you are "running as long as you physically can".

To compete successfully in most events, you need strength and endurance in addition to speed. A training plan like this does not develop either.

Sounds like a good way to get injured.

I was looking at Mike Mentzer directly, and thought it could carry over to long distance running.

I think what your asking is more hard workout oriented. Say you run 2k hard and your hitting 3k effort. Maybe it takes 5min before you feel good enough to go again and you only get 1600 at relatively the same pace and so on. You can do workouts like this but if your truly hammering these you can necessarily be doing them all the time. There was a 90s/2000s runner (forget) his name where training for world xc he would start every interval hammering these first 400 before settling in trying to maintain pace over the whole say 1600 interval. And over time his body was able to adapt and those times for the whole interval dropped as his body learned to handle the increased lactate levels early.

Isn't that what racing is for?

There are plenty of training sessions that get close to this anyways. You can do 6 x 1k training for a 5k with a decent amount of rest towards the beginning of a block & then, closer to your goal race, do 3-4 x 1600 w./ full rest. You're basically at your max. Obviously you can't do this every day for the reasons everyone has mentioned -- burnout/injury. Lactate is sort of the obvious reason if you just go as hard as you can in a training session why you won't get past the first rep. Even with a ton of recovery you're not going to match your 1st, race-like, effort.

I’ll interpret your question as why not, say, for 10K training run 10K’s at the goal pace or as close to it as you can and then rest as long as needed to rinse and repeat. Presumably doing the exact activity you are training for should make you better at it, right? The answer is No because the primary training stimulus to improve vo2max is to spend a significant amount of time at a significant fraction of your vo2max (but not at the very max), which means increasing mileage without getting injured in the process. There is a lot of empirical evidence for this and we have a pretty widely accepted physiological models of underlying mechanisms (like capillaries, mitochondria, enzyme activity etc) of why that is so.

The Mentzner analogy even taken as-is doesn’t suggest what you are thinking. In lifting, the primary stimulus is to train close to failure, which Mentzner provides. The end goal is bodybuilding or a single 1RM lift, which is different from the training itself. Similarly, in distance running like a 10K, running the 10K at the goal pace is the expression of fitness, not the best way to build that fitness.

Because it may kind of work for sprinting, but for long distance running it is inefficient.
I am simplifying a lot, but for long distance running, the optimal training tries to maximize the amount of running spent at a certain pace. When you run a sub-maximal effort, you recover faster and you can run more, while still getting essentially the same training stimulus.
To make a stupid example, assuming that it takes 1-2 days to recover from a 10K race. If you train for the 10K by just racing a 10K and the resting and repeat, you may be able to run three or four 10K races a week, for a total of 18-24 miles/week.

I once trained someone for the marathon in a variation of what you mentioned. They ran one or two miles once or twice during the week and the on the weekend they would run long. Starting at 5k and topping at 30k before the marathon.

Did that training method work?

Usually end up on the toilet with diarrhea when I do that

Think of it this way. A lactic acidosis session/race will drain the endurance battery. However, aerobic running will charge the battery. Therefore, you have to balance how much you drain the battery with how much you charge it:

This isn’t exactly what OP is suggesting maybe, but I think in Part 3 of the old Hadd document from letsrun kind of gets at it

https://www.angio.net/personal/run/hadd.pdf