To be clear, I am not emailing people to pat myself on the back and see how loved/lovable I am. I already know the answer to that question, which is "not much": I'm not sure what other people's success rate with cold emailing POIs, but mine has not been great. I have researched almost 50 professors, emailed ~20 of them (over several months), got responses from half, and positive responses from half of that half. I don't feel all that comfortable only having 5 schools at this stage of the process, so yes I am emailing people more on the fringe of my interests. Admittedly in the case I probably extended too far..