They werent usually angling for a promotion.
The anxiety wasnt always unwarranted either. If you're in tons of debt, hate interviewing and work for an organization that doesnt care for people this isnt a wholly irrational strategy.
If your job is _that_ important, you might not get promoted away, but you'll get the salary as if you were and then some.
I take it as a rule to not ever mention that you're leaving somewhere until you're leaving and then follow through.
I see "wanting to leave" as either absolute ("I hate this company, no amount of money can make me stay") or relative ("I could make more money / have less work / do more interesting stuff elsewhere"). The latter can totally be shifted by adding significantly more money, at least for most people.