More so weak glutes and tight hip flexors usually. Those exercises hit the glutes super hard if you do them while maintaining a neutral spine. However it wasn’t enough for me, my glute medius was weak and so I needed to add in yoga moves and side planks. Ddpy is the best for back pain!
I've started doing Iyengar Yoga a few weeks ago (but the specific school doesn't seem to matter in that regard), and believe me, it's the hardest workout I've ever done (to my shame).
I'm certain I'm building muscles there. The focus seems to be stretching of hardly-ever-stretched muscles, but there are all kinds of postures that are basically body-weight exercises.
Yoga asana incorporates a lot of body weight exercise, so yes you’ll gain a lot of strength in a practice like Ashtanga or Iyengar. A lot of asanas that don’t look complicated require very subtle muscle development, but you certainly can’t do Astavakrasana or press up into Pincha Mayurasana without tons of strength.
For lower back I’ve found practicing Salabhasana, Dhanurasana, or Urdva Dhanurasana have helped.
As I mentioned, my go to is ddpy which is “not your mamas yoga!” It incorporates a lot of calisthenics moves and gets the heart rate up for a great workout which builds strength.
How would you feel participating in a message board site for yogis who are on HN? I think the mix of intensity + curiosity & openness to the unknown would foster great conversation threads