I am not sure about the difference between being on raw vs cooked food and training, but as a trainer, I would suggest "nervous system exhaustion" is a non-concept.
The difference is huge I know from personal experience! Nervous exhaustion is a very real thing.
The body will get weaker before it gets stronger, and you have to work through that.
Not necessarily true. exercise damage the body so yes that is weakening to a very limited amount. However the first thing the body does is recover. only after
full recovery are strength gains possible. If you have an exhausted nervous system, rest, sleep, and good nutrition are the first requirements. Only when recovered to a reasonable degree should exercise be resumed. And at a very infrequent rate, allowing plenty of rest.
Strength gains are the quickest gains a beginner will develop, and high frequency is integral to learning motor patterns and developing strength.
Yes those are the fastest gains because neurological efficiency improves. this is only possible with fully functional, fully recovered nervous system. Frequency is linked to intensity, is one is high the other must be low. And it happens to be true that it takes high intensity, and thus low frequency, to develop strength. Try doing both and you will overtax your recover ability/nervous system.
If you are exhausted, even then you should be able to train. The best way to train through this period is to do concentric-only training. I remember for a period I trained maximally, the same movements, 5-7 days a week like an olympic weightlifter would. The several times my numbers started dropping I would simply do concentric-only training for a few days before switching back and this worked for me, and I came out much much stronger.
Obviously I don't expect anyone to train 7 days a week like me, but everyone should be doing low volume training as often as they can unless they have a specific goal such as sports or bodybuilding.
Concentric only training is always a mistake regardless of circumstance. The eccentric part of the movement is safer(no jerking possible thus no impact forces) and more productive in any type of recovery/rehabilitation. This has been proved numerous times. It should however be noted that eccentric training is harder/intenser so if you don't reduce frequency you will overtrain again.
Training 7 days a week is never more productive than training less frequent and harder. No rest days are a good way to, over time, totally exhaust the body's resources.