It's absolutely appropriate in the workplace. I'm not going to be mean or snide, but if I'm asking you a reasonable question and you're not answering it, I'm going to be increasingly direct. If I need information from you to do my job, and you're withholding it from me, then you're the one acting inappropriately.
> but if I'm asking you a reasonable question and you're not answering it, I'm going to be increasingly direct.
And herein lies the flaw in your approach. It's reasonable to be annoyed that you're not getting the answer, but it doesn't mean your approach is helping you get there. It's the equivalent of "If someone doesn't understand me, I'm going to shout even louder" or "I'm going to use the same words, but speak even slower".
There's no good reason to think that more directness is more effective.