Over the past few months I’ve contacted around 10 potential advisors at various schools of interest, and the only professor who has gotten back to me told me to wait until I was accepted if I wanted to work with him. My email strategy has been reading over papers from a professor and crafting personalized emails explaining who I was, why I was interested in their research, and asking if they had time to discuss what they are working on. Since many professors instruct to not even contact them until after a student is accepted, and many others don’t respond to prospective students, is it even worth trying to reach out? Is it still too late to keep trying to get in touch? It’s difficult to justify spending the time to look into a professor who doesn’t respond, but I keep hearing that it’s important to contact professors of interest before applying.
What I would do, and that is what I actually did, is to send email to those professors that are actively looking to fill an open position. As I have experienced, there are a lot of open positions out there and there are many resources (here, here, here, and here) to find out a specific position (PhD, postDoc, fellowship...), the country/city where you will work and what is the project about.
Ususally for PhDs these notices comes in two flavours: there may be many open positions which will be filled through a complex process involving a commission examining the applicant's CVs and then contacting those who passed the first selection, or a professor which posted an open position. In this second case, as I experienced, gives you many more possibilities and, more importantly, you can directly contact her/him by email and you will have a closer contact with whom might be your future supervisor.
It obviously is a strategy. It is viable to a certain extend. There are issues of course. You have read similar entries about cold-mailing from this webpage. People send cold-mails, usually generic to hundreds of people. As a reaction, these recipients started to ignore e-mails of similar nature. Now, I know your e-mails, as you describe, is hardly generic. But the recipent will not know that, if they don't read them. Odds are they won't. Your strategy pours a lot of time into a single e-mail that won't likely get read.
I would instead suggest transfering such e-mails through a more reliable source. Maybe your proffesors have collabrators that you may be interested in and you can prove to your proffesors that your interest is geniune and they may communicate your request.
Or I better option would be to devote your time to search for more people / universities. There are a lot of good researchers in relatively easy to get in places. Or certain side of an easy to get in university might be much stronger than their overall department or university. I personally think, those are the most efficent time investments.