Talking to "product managers", managers and various stakeholders everyday, the problem is at the times when these otherwise good people are disconnected to the rest of the organization and have no operational clue. Then they will demand deadlines, push dates backwards, do all sort of non-intentional self-sabotage to the org. They might get their thing done, badly, while hurting the rest of the organization and creating unhealthy competition. When goals are accomplished, they often are unable to even get the value out of the thing they wanted in the first place. These same people won't be able to prioritize when given the choice, and basically just want it all now, again like little toddlers, with checklists!

So what do you do? Only healthy thing is to push back, give explanations for what is required before work can begin and have good relationships with all parts of the org yourself. Insulate the toddlers. If they need a PM, they gotta provide a budget.