Looking for new gigs is currently the new normal regarding promotions anyway, according to HMW. Since companies have long shown that have no loyalty to their workforce and will lay them off as soon as they need their numbers to go up for shareholders.
And new hires to positions get paid better than promotions from within to the same positions. So it's better just to routinely keep sending out résumés to openings.
So the no promotions threat is mostly a paper tiger.