1) Mechanical Load
Mechanical Load is necessary to induce muscle hypertrophy. This mechanism involves but isn't limited to, MAPk/ERK, satellite cells, growth factors, calcium, and number of other fairly understood factors. It is incorrect to say "we don't know how muscle grows in response to training". The whole point of the HST book is not to discuss HST, but to present the body of research explaining how hypertrophy occurs. Then HST becomes a relatively obvious conclusion if your goal is hypertrophy.
2) Acute vs. Chronic Stimuli
In order for the loading to result in significant hypertrophy, the stimulus must be applied with sufficient frequency to create a new "environment", as opposed to seemingly random and acute assaults on the mechanical integrity of the tissue. The downside of taking a week of rest every time you load a muscle is that many of the acute responses to training like increased protein synthesis, prostaglandins, IGF-1
levels, and mRNA levels all return to normal in about 36 hours. So, you spend 2 days growing and half a week in a semi-anticatabolic state returning to normal (some people call this recovery), when research shows us that recovery can take place unabated even if a the muscle is loaded again in 48 hours. So true anabolism from loading only lasts 2 days at best once the load is removed. The rest of the time you are simply balancing nitrogen retention without adding to it.
3) Progressive Load
Over time, the tissue adapts and becomes resistant to the damaging effects of mechanical load. This adaptation (resistance to the stimulus) can happen in as little as 48 hours (Repeated Bout Effect or Rapid Training Effect). As this happens, hypertrophy will stop, though neural and metabolic adaptations can and may continue. As opposed to hypertrophy, the foundation for the development of strength is neuromuscular in nature. Increases in strength from resistance exercise have been attributed to several neural adaptations including altered recruitment patterns, rate coding, motor unit synchronization, reflex potentiation, prime mover antagonist activity, and prime mover agonist activity. So, aside from incremental changes in the number of contractile filaments (hypertrophy), voluntary force production (i.e. strength) is largely a matter of "activating" motor units.
4) Strategic Deconditioning
At this point, it is necessary to either increase the load (Progressive load), or decrease the degree of conditioning to the load (Strategic Deconditioning). The muscle is sensitive not only to the absolute load, but also to the change in load (up or down). Therefore, you can get a hypertrophic effect from increasing the load from a previous load, even if the absolute load is not maximum, assuming conditioning (resistance to exercise induced micro-damage) is not to extensive. There is a limit to the number of increments you can add to increase the load. You simply reach your maximum voluntary strength eventually. This is why Strategic Deconditioning is required for continued growth once growth has stopped (all things remaining equal).