Assuming that someone else is available to do the low priority tasks when they get dumped. Otherwise you get managers wondering around asking why you’re not doing unimportant work. When you tell them the reason you’re not doing unimportant work, is that it’s unimportant, and you’ll get to it when you get to it, they decide that suddenly it is important after all and you need to do everything with equal priority.
Assuming that someone else is available to do the low priority tasks when they get dumped. Otherwise you get managers wondering around asking why you’re not doing unimportant work. When you tell them the reason you’re not doing unimportant work, is that it’s unimportant, and you’ll get to it when you get to it, they decide that suddenly it is important after all and you need to do everything with equal priority.
It’s like you’ve never worked in an office.