Nice post Piotr. As you're painting the picture of ideal PM, let me add one more trait to it: the ability to switch perspective from the strategic one (understanding how a particular product fits into the strategy and business model of the company - it's not always that obvious) to the operational one (ability to make short-term decisions quickly, solve problems and plan/organize the work for the team). And of course it's never enough to emphasize the soft skills.
That's right idea PM needs it, but you need to start from something. It isn't easy to have all of those
characteristic from the beginning. It's all about learning and trying.
