Priorities work - but only if used wisely
The word priority is used in so many different ways that it can make anyone confused, and it can be used for so many different practical purposes (with different kinds of real consequences).
I like the simple and intuitive definition that if anything makes me "excited or anxious or watchful etc" (usually due to its importance or urgency, value, risk, credibility etc etc), then the "priority" is high. And conversely.
Essentially, in practice, priority to me is just another way of saying "I want to see and consider this more often". I find it very useful to mark my tasks and projects in this way, and base my review frequencies etc on this.
I do not infer any time limits, nor any element of "must do this before I do that" from my definition of priority.
Priority, in the sense I use it, is just one of all the factors I weigh in mentally when selecting which tasks to do. Context (and the effort of switching contexts), energy and priority etc all needs to be looked at as a whole.