Constant interrupts is a sign something is wrong.

Look at construction sites. Do you see the manager telling the dude on the crane lifting some beam up that he has to stop mid-way and go do something else? Never. If you plan and execute well this should not be a problem to start with. If it's not a problem then polling or interrupts doesn't matter. Plans can change but they don't change every hour.

The customers behind your boss generally don't have new tasks every hour either. They could require service or have some sort of problem. When your car breaks down do you call the guy who designed it?

If you're building software, and you're constantly (hourly) shuffling priorities or engineers are constantly fixing the software for customers, then that's the problem that needs fixing. It's not a tooling problem.

EDIT: In the days before Slack and being constantly plugged in people were a lot more conscious about interrupting others and we had less interrupts. The reason we have more interrupts today is that it's just too easy to interrupt people. Not because we really need them - we don't. It makes us a lot less productive.