Hello Allan,
For me, anyway, Systems Thinking is the Big Picture. Many subsystems make up the 'big picture' and viewing them independently is the problem under linear thinking. The systems are interrelated, dependent on each other. Correlations exist, and sometimes not directly, but influencing one has impact on another or others. This speaks to your point of having a concurrent approach to system optimization. Working to optimize the Big Picture requires careful understanding and manipulation of multiple subsystems. Knowledge of the System (Big Picture) is key and having the correct Theory. This is a difficult objective, and why, IMHO, many organizations abandon this theory. It takes too much work and results aren't instant. Many organizations focus on the Short Term successes.
Linear thinking leads to suboptimization of subsystems. It lacks the Big Picture understanding required for organizational success. As Deming is careful to point out, precise optimization is not necessary nor desireable. In short, perfection isn't necessary to achieve good organizational success, nor profitable.
Regards,
Kevin