The Myth of Core Stability

I’ve never dealt with back pain so I can’t say for certain whether the ‘tummy tuck’ and trunk bracing exercises will help.

But what I would say is, if the muscles you mention are strengthened & help with stabilising the spine along with the multifidus/inner obliques etc) hence gaining better posture, then surely the patient with lower back pain must benefit from that.

It’s not the be all end all. Having a beer gut is known in some circles to cause chronic back pain. By not addressing that particular issue, all the spinal strengthening exercises in the world probably won’t help you.