One of the failures of HEMA in my opinion is the community's aversion and resistance to incorporating standard athletic strength building in to their training. They seem to be of the mind that just doing the activity more and more is the key to success, but every other sport on the planet seems to realize that you have to go well beyond the specific movements associated with the sport itself to improve overall athletic performance. I think you'd see much more powerful and skilled athletes if they stopped being squeamish about more traditional training incorporation in to their routines.
I generally agree with that, with maybe a slightly different "why" of the training / competitions. I think we're a bit of a specialty in WMA/HEMA, as we have a few different groups of intent: athletes, the scholars, and the system-gamers.
The athletes are a small set; they train hard, they compete, and they want to win. It's about winning by being at the top of your physical conditioning. The historical side isn't as important as winning.
The scholars seem to be a large part of the WMA/HEMA group. We are re-interpreting a long lost art of combat, and in pursuit of historical context. They are in pursuit of the techniques, the experience, the practicality of "does this interpretation actually work?". It's about the history and knowledge, not physical conditioning. Sometimes it's even less about a win or loss than it is trying to apply proper historical technique in context of an actual duel. Additional variety in tournaments like cutting and tournaments really stress the scholarly aspect.
The system-gamers will eschew any concept of historical technique just to win. They compete to win, not by skill or conditioning, but by playing the system. Wild single-handed swing aimed at the knees with no technique or control for every single point? Eh, point is a point, "cheap shot" or not. Luckily this is going away substantially with Longpoint style rules, but, the mentality of "how do I work this system to my advantage so I can win?" is still different as compared to the athletes and the scholars, just as tournament karate is compared to actual battlefield martial arts.
That doesn't apply with regular/mainstream modern sports. Almost nobody cares about the historical context of football (baseball, soccer, etc). There isn't much gaming of the system in football because everyone is doing exactly the same thing for the same reason. There's no "cheap 2 pointer" and "historically accurate 2 pointer". The only things you have are physical conditioning, skill and luck; the rest just doesn't apply.
We have overlaps; scholars in good physical shape, athletes with an interest in the scholarly aspect. I'm no athlete, and I have a health issue with somewhat reduced lung capacity and blood flow, compounded with previous injuries (my knees suck). Doesn't matter. I do it because I love the experience, I love seeing the excited kids (and sometimes adults) watching two knights in full armor dueling it out, and I love the historical aspect of it all.
On top of that, extreme physical conditioning would take away my time from working on armor, furniture, my car, my house, reading, etc, and is just a lower priority item for me. I hit the treadmill or weights when I can, but it's inconsistent. I don't diet like I should, either. To those who can and do, I respect the amount of time and effort it takes!
(Sir Edward, can we split this topic?)