This is truly a mistake. I did adopt the pose of the bastard boss in a tongue-in-cheek fashion (for example breaking a printed vacation request) and never got nothing but a good laugh in response.
But this is toxic behaviour an in a multicultural environment can be damaging to the team and personally devastating. Just don't.
It's awkward to LARP that it is all at your whim - because at some point someone will ask too much in a vacation request and you do suddenly need to explain the factors very not much in your control (before proceeding to then rip up their request, of course ;))
I've only ever once been denied a request for annual leave, and I don't recall anyone I've told the story of that to ever having had a similar experience.
One place I worked had spelled out explicitly in the employee handbook that "if you want to take more than three weeks off consecutively, please give us at least two weeks' notice". They also discouraged people from scheduling holidays to accommodate deadlines on the basis that the deadline was probably going to shift, so it wouldn't help.
But this is toxic behaviour an in a multicultural environment can be damaging to the team and personally devastating. Just don't.