There is probably not a single set of exercises that could be better for your back. No, spinal injuries are not necessary. When done correctly and with good form, these will strengthen your back and protect your spine.
If you don't train/strengthen your lower back, you are inviting disaster.
What's dangerous is the trend for people to do ab work ad nauseum and then not do any back work. Can you say 'imbalance'?
If you want an exercise that can directly contribute to your core strength by working both your abdominal muscles and lower back, look into the head bridge Ė a bridge where the weight is placed on your forehead and not supported by your arms.