"My best powerlifting accomplishment in the 275-pound weight class was a 1,000-pound squat, 675-pound bench press, 700-pound deadlift, and a 2,375 total. No, I wasn't strong at all! Sure, I could waddle up to the monolift and squat, but I couldn't do anything else. Really, all I could do was squat, bench, and deadlift." (Jim Wendler)
Some of the muscles are a lot stronger than others.
These muscles tend to act as prime movers, they iniate movements.
Smaller muscles tend to act as stabilizers, they contract but do not produce any movement.
Consider the overhead press.
The anterior deltoid is a prime mover and the posterior deltoid is a stabilizer.
Weak posterior deltoids relative to anterior deltoids cause rounded shoulders. The overhead press may cause such an imbalance. If you do it heavy and fast the anterior deltoids get a lot of excercise but the posterior deltoids probably not so much.
I have done Yoga twice. The movements were performed slow and controlled. There were no momentum involved so a lot of stabilizing muscles had to work in addition to the stronger prime movers. There were also a lot of movements. In my opinion Yoga makes the weaker muscles stronger and does little for the stronger muscles. But I think that is great. I do not want 90 % of my muscles to be very strong and 10% to be weak. I believe that is a recipie for pain and dysfunction. In particular the ball socket joints in the body, the shoulder and the hip, requires balanced musculature around them in order to have full range of motion (ROM). Judging from the Starting Strength forum there seems to be many who experience sore shoulders from the benchpress. I believe a "no pain no gain" mentality can be harmful. Yoga also makes you more flexible. I believe this is thanks to alternating between stretching thereby increasing ROM and strengthening in the newfound ROM.
However I find Yoga boring and believe that lifting weights can also be done in a "Yoga" manner. The effectiveness of Yoga does not stem from it use of indian names for postures nor from its use of only the body as weight. If you do the overhead press with a light weight and hold it at the top and gently swing the barbell back and forth slightly focusing on control instead of power and also focus on your breath; that is Yoga!
Programs like Starting Strength focus on a few most effective excercises in order to get say 90% of the muscles stronger as fast as possible. For same reason they also focuses on lifting heavy. I would argue that if you are not only interested in getting stronger but also enjoy being painfree and have good mobility; you are better served by using many variations of the main movements. One day you may backsquat, the next day you do lunges. From what I understand lunges train stabilizers more but is not such a good massbuilder as the backsquat. You are also better served by doing some lifts heavy and others light and controlled. First you do the overhead press heavy for say 3 sets; then you do it light and controlled for another 3 sets. The light sets may be performed in between heavy sets to save time.
Is what I suggest a feasible approach or must 90% strength training be kept separate from mobility work or Yoga?