Last year, rather late during the MSc application cycle (after one round of funding was allocated - tardiness due to an abrupt change in my life situation), I emailed two professors from two schools that I most wanted to go to. I had perused their webpages and decided these professors had the specific research interests closest to my own.
My reason for contacting them before finishing my applications for their respective schools was that the applications included a large section for specific research questions that I wanted to investigate. So, I emailed these professors asking a bit about their work, because their webpages of course featured surface-level stuff.
One professor was very receptive and invited me to Skype with her so she could better explain herself and I could ask her questions. With her support, I was able to write an application that met her standards quite quickly.
The other professor told me - paraphrasing, of course - that he was too far into the process of choosing a new student for his research group to spend time helping me finish the application.
Let me be clear that the latter professor didn't say any harsh words and I have nothing bad to say about him. That said, the purpose of my question is to decide whether it's better for me as a prospective MSc student to email professors ahead of time like this. Was the latter's rejection likely due to my tardiness rather my emailing him? The more receptive professor made the point that she always wanted to have prospective MSc students write their own research proposals and get her approval before submitting the application. Is this common? If so, then I guess reaching out beforehand is a good thing to do, but earlier in the application cycle?
Thank you.