Thanks for sharing your opinion. I think I have a slight different opinion than you. In my humble opinion and journey as a PO during the last 8 years, I have come to some conclusions:

• Value: as a PO we must understand what value means, therefore leading the team towards a way of maximizing it. In order to do that, we must understand our audience, meaning that we discover the hidden problems and can solve them;
• Measuring the value: it is true that we may not be able to measure the value on all PBI level, but we should at least be able to group them into a theme or epic in a measurable way. We should not start developing something if we cannot clear understand how we will measure the outcome of that;
• Sprint Goal: the PO defines that as a guidance to the team, which will lead them to collaboration, in case during the Sprint the team discover some alternatives to reach the Sprint Goal, they can and should create another PBIs for that, they are committed to the Goal, not to the tasks itself. However transparency is one of the main parts of Scrum, so they should practice that by sharing their suggestion with the PO, I am pretty sure that this is healthy and sustainable.

There are many scenarios where there is no role of Product Manager, therefore the PO must takes that responsibility. The role of the PO is so complex that it is still not understood totally by the companies, but one principle is always true, we must maximize the value for the business, the way we do that may vary from company to company.