It's easy for us in fitness (inclusive of both exercise and nutrition) to think of the human body in mechanical terms. Our analogies and metaphors are meant to evoke a sense of genes, biochemical pathways, and living cells as rigid clockwork and orderly assembly-lines making up a larger machine.
The best way to describe a non-equilibrium system is to think of it as a "whole" rather than a set of "parts" that just happen to work together. This is not easy to do. The machine analogy is pervasive and the internet fancies itself scientifically literate by way of fantasies constructed from Pubmed abstracts, all of which leads us to think that the parts, rather than the web of relationships, are important.
Complex systems, of which life is a particular instance, exist in the relationships between many individual parts acting in together to create a whole. We discuss hurricanes by describing the properties of hurricanes, like wind speed and the shape of the eye, rather than zooming in to all the water droplets. These properties give hurricanes a distinct structure, but that structure exists within incredibly violent, uncertain, and constantly-changing conditions. The water droplets work "up" to create the hurricane structure, and the hurricane structure works "down" to keep the water droplets moving in that pattern. You wind up with a system that is inherently unstable and, because of that whole-part relationship, orderly in spite of that.
How this ties back to fitness may not be immediately obvious, but there are two related claims that prompted my thinking on this matter:
i) Risk of injury increases with the amount of exercise done.
ii) The amount of exercise you can do depends on your ability to recover from it.
For these instances we can treat "amount" as being a number of workouts done each week, so that three workouts per week represents a larger amount of exercise than one. Volume and intensity will matter, but for simplicity let's just look at the frequency.
Both of these claims are widely believed to be true, commonly cited as factual, and make up the core of many a workout program. I don't believe either of them is true when taken at face value, and the reason is precisely because they rely on the mechanistic analogy rather than seeing the living body "as it is".
Since complex systems adopt a condition of "unstable stability" and thus have no equilibrium condition (the way a factory or a clock would), the same rules don't apply. The same hurricane can exist in hundreds or thousands of states during its lifetime. It can grow, shrink, move faster, slow down, decay into rain clouds, and transform back into a category 5 death-engine. As long as the unique whole-part relationship exists, you have a hurricane.
The same metaphor applies to your body. It's not quite right to say that you have a "reserve" of recovery, as if you just call down to the store room for power-ups after every workout. You haven't depleted a battery; there is no battery.
When you undergo any major stress-event, you throw your body out of its comfy state of stability, and it scrambles to bring the house back into order. This process is not fun, which is why you feel beat up and "worn out" after a hard workout. But "exhaustion" and "fatigue" are not the right words for this condition. Your body is coping, not exhausted.
The feeling of beat-up-ness (which applies equally to physiological measures of stress, including serum levels of testosterone and cortisol as well as HRV) represents a "pseudo-limit". It may feel as if you have reached your limits, and your physical state will show signs of stress, but this condition has far more to do with the feelings, sensations, and emotions generated by your body than it does your genuine physical limits.
Imagine you walk into a maze and every step you take changes the layout. That's how a complex system works. When you alter any piece in the whole, the whole changes along with it. The whole-part relationship is stable, but not on terms that fit our machine analogies.
If you envision your body in mechanical terms, you can map injury risks and recovery a like along a nice orderly inverted-U curve. One workout means X risk, three means a risk of X+3. Nice and linear. But you aren't mechanical, and moving from one to three sessions does not simply move you along the pretty graph -- it changes the graph's shape.
Doing more may not involve any increase of risk at all. It might even reduce the risk (yes, I mean to say that training more often may be inherently less injurious than the typical once-or-twice-a-week split methods).
The simple notion of "recovery" is concerned with pieces; the genuine limit requires thinking of the whole, the way the whole changes according to what you do. What can your body really do, if you ignore the "I feel bad" signals and just keep training anyway?
The whole has limits, obviously. Hurricanes run over dry land and starve to death. Living bodies have very real limits to the amount and magnitude of disruptions they can take from the environment. In that vein you cannot endlessly add volume and frequency to your workouts (whether strength or endurance) with no repercussions. Eventually you reach the limits of the whole's ability to adapt.
My argument is that these genuine limits lie well beyond what is allowed by the pseudo-limits implied by the simple notion of recovery. The machine implies snapshots and "more is less" relationships.
We need to focus instead on the "second-order" effects: the behavior of the whole as an ever-changing system, a system which can experience positive feedback (wherein you "do more to get more").