I'm not sure if on purpose is the right word. I think that if it is an email, did you set boundaries upfront? For instance if I email my T, I know that anything I email her she will discuss with me at my next appt. Only once has she responded and that was a shock for me and she even stated this was not normal for her.
If she does answer, it is the weekend, maybe she is taking time with her family, away from email, enjoying some much needed rest?

If I have an urgent matter I call and make a same day appointment. My T knows I only do this in a crisis and she will find a spot for me.

Now back to your original question, yes I think they do things some times in a therapeutic matter. For instance, me and my T were hitting our 1 year mark, and she brought up the fact that maybe she and I were not the right fit and maybe I needed to see someone who was a better fit for me. Of course this brought all types of emotions of abandonment, anger, etc, up front.
But it also made me make a decision, I had been sitting on the fence. I either let her help me and finally trust her, or I needed to move on. What I came to realize is that she wasn't threatening me she was trying to help me understand that we were not making progress and maybe we were not the right fit, or maybe I was the one that was blocking the help.... August was one year of Seeing her, and we are just making progress now. If she had not done that, I don't think we would be any further than we had been before she did this.

So yes, I think they do things, to help us, that at the time may anger us, frustrate us and bring all sorts of emotions out of us.

I also believe that T's are human and sometimes just need a few hours break, a weekend with their family or just some time away from all the ways their clients/patients can reach out to them....

Just my humble thoughts....