Mountain Climbers on Core-Tex are an incredibly demanding metabolic exercise that challenges your cardiovascular system and your overall stability at the same time. The arms must drive the platform as fast as they can and the legs must keep up. Opposite arm and knee drive at the same time, similar to running. See how many you can do in 30 seconds.
You can't treat thoracic mobility like hip, or shoulder or ankle mobility. The hip, shoulder and ankle are individual joints. The thoracic spine is major body segment with multiple joints involved, plus the neurologically sensitive diaphragm.
Stillness and being propped in "proper" position is not the solution to avoid back pain while sitting. Mico-movements give the brain and biology what they need to stay healthy and do more than any ergonomic chair will ever do.
Sure the glutes are responsible for those big squat lifts and powerful hip extension. But they also play a critical roll in the overall function on the hip joint and pelvic control in day to day activity . And most day to day activities involve a period of unilateral loading of a limb. That is why the single leg glute bridge is such a great exercise.