PMs should also be a lot more focused on the business’ goals than most PMs are. It’s necessary but insufficient to solve problems for your users. Solving those problems needs to translate into value for your company too.
Strong, product-minded Eng/UX partners are essential in enabling that.
I'll say it depends on the size of the product. If you're dealing with say ERPs (Oracle Fusion Apps, WorkDay, SAP, etc), a PM can't own an entire product. Instead, they'll own multiple features where each of those features are complex in themselves and being ERP typically involve integration with multiple other products.
But I agree with the general thrust of your point which seems to be that the PM should own something 'significant'