Exactly. I would respond to this policy by never taking any vacation time ever, or, at the very least, feeling guilty every time I did.
If a company had a "no vacation policy", and when pressed about it, they said "just get your work done - we don't track vacation time", how much vacation time would you plan to take in your first year there?
When you're there, you realize that nobody ever takes vacations. Can you still justify that three week long trip to Asia that you had planned? I mean, you can always find a new job, but you've already sunk a ton of time into the company. If instead they said that you get three weeks, at the very least you get paid out for it when you leave. It's also easier to get a direct answer for "do people take their vacation time?"
As an aside, but I think your point "they [think they] are irreplaceable or are in continual danger" is a pretty good point for encouraging extended vacation - if you can't survive for two weeks without someone on your team, something needs to change, and that can be a good way to identify those people.