Hello Blaze,
interetsing path this thread has taken eh?
In a full, general yoga practice {sidebar: please know my definition of yoga is not synonymous with asana but for this thread we are clearly talking about asana} I do not see a need for hindu squats and pushups. The question I would want answered would be:
“What do these two things do for you biomechanically/anatomically and how/why was that not addressed in the asana practice?”
The first “event” is simple hip flexion and extension.
The second “event” is quite similar to the action moving from Adho Mukha Svanasana to Urdhva Mukha Svanasana via Phalankasana or Chaturanga Dandasana.
So these things might be great for combat preparation but seem, based on the above, unecessary in the presence of a robust asana (yoga ) practice.
As far as integrating Asana (yoga) with other things I don’t find an issue there. I do go to the gym. When I go I usually row and I do so with a certain posture and form and breath so I am squeezing as much “yoga” out of it as I can. The rest of what I do is in integrity with my practice: some aided twisting, some hanging, some backbends. The action typically not built in to asana practice is this latisimuss dorsi rowing action or door-handle pullling. And those of us with wall rope systems in our studios are even finding ways to add that to asana. I don’t believe there’s a way this is incorporated into many of the other practices.
If you find weight training to inhibit your yoga practice it may simply be how you are weight training. Though I frankly do not advocate it since weight training seems to strengthen while shortening.
If it is running you want to do then I advise really working hip adduction, abduction, internal and external rotation in the asana practice for proper balance of the body.
I do hope we will all effort to keep in mind that every asana practice is not OUR asana practice. For this very reason I use care with statments that might be perceived as absolutes. Just as we are ALL not sitting around in a cave neither are we all using a towel to mop up the sweat from our brow.