I have noticed a few other problems in the theory (specifically that ‘muscle fibers’ only learn to be strong in the specific movement trained when high tension is used, but ‘just get strong’ when maximally hypertrophied).
The first pertains to the central drive theory (I don’t know who first hypothesized it, but I read it in Charlie Francis’ work). This states that improvements in some aspect of the CNS’ ability (in terms of region) translates to improvement in the ability of CNS in other regions of the body.
For examples of this, see comments about Ben Johnson (a man who could certain throw a punch in his day, due to the whole spectrum of non-specific (to punching) training means, done at a very high intensity) benching more closely to competition in order to maintain high CNS stimulation, or just read about Dan John’s one armed work (during injury) leading to a MUCH lower billateral strength discrepency once his injured wrist allowed training.
The second problem pertains to method of strength development. According to Siff (and I am confident that others agree with him), there are three methods to increase displayable strength (not str-end, not power-end, etc). These are the improvement on MU recruitment (turning on more total muscle fibers-using the discontinuous innervation model), rate-coding improvement, and fiber cross-sectional area increase.
Optimal training methods for the first include explosive movements, such as med ball throws, vertical leaps, light speed squats, olympic lifts, etc. Optimal training methods for the second include straining efforts against high resistance, generally for a low number of reps (due to the reality fatigue byproducts inhibit CNS function). ‘Optimal’ training methods for the third are highly open for debate (as can be seen on the ‘Building a Better Body’ forum).
This third category is likely where most 5x10 loading parameters fall. This method is effective and required IF the athlete has maximized his(her) ability to recruit multiple motor units, and optimized his(her) ability to sustain firing those motor units (I say optimized because, in a punch or any other high speed movement, there comes a time, due to short duration, when more ‘twitches’ don’t have any effect, as the movement is complete before they are used). These developments ARE NOT specific to the movement pattern, but are an intrinsic feature of the trained motor complex (all available MU’s in the body region).
As such, the ability to rapidly generate force in the elbow extensors positively corelates to increased potential punch force, as does improvements to generate force in almost every muscle of the body (as a punch truly is a full body motion). Where your understanding of specificity is getting muddled is in the expression of force. The reason why practicing flat bench presses most greatly improves flat bench press performance is because every physical skill has a specific optimal time-position-force relation between all the muscle complexes involved.
So when you say a maximally hypertrophied muscle would produce more force then a muscle with lower cross-section, in an absolute sense, you are correc. The same holds true for the other two factors affecting motor complex strength. As such, ANY increase in the ability of a motor complex to produce strength, so long as it is limiting factor, improves the potential to produce punching power. The key here, for each body link, is force production potential. For the whole body, it is then skill development (meaning force balancing/timing/directing).
For this, it does not matter is the arm (or any other body segment, the example holds) is 18" or 15" in circumference, if they both are capable of producing 1000 N of tension in the elbow extensors, they both are equally capable of producing force to add to a punch. In fact, the smaller arm is probably preferrable (I know, I just said it might be better to be smaller, the horror) because, owing to its invariably lighter weight, would allow greater acceleration around the shoulder joint due to F=ma (sorry, I don’t know how to get the angular ‘alpha’ from this keyboard). This holds true for ALL joints.
So, in conclusion. Force is non-specific. As such, absolute force production is non-specific. Skill development through practice, with the available force potential, leads to punch power. Improving either of the two factors (skill or absolute force production) is highly likely to increase punch power. Final question, who would you rather have hit you, an Olympic level weightlifter, or a high school welterweight gold-gloves boxer (assuming that the weightlifter is in the same weight class)?