Context: I want to do my PhD in Hong Kong. Only one University there (University of Hong Kong) explicitly states you need to contact a supervisor and discuss a research proposal before you apply. The others, at least in my field, do not even require a research proposal for your application.
Regardless, I obviously am trying to get faculty members to agree to supervise me and discuss PhD topics to strengthen my application and ensure that a suitable supervisor is available.
The trouble I am facing is that only a few of those I have emailed have replied, and the ones that did reply said they already had too many PhD students or weren't taking students on at the moment. Looking at current PhD students, >95% of them are Chinese so I suspect part of this might be unwillingness to take on a foreign student (or just preference for Chinese students) despite Hong Kong being a very multicultural city.
I would like to live and work in Hong Kong after my studies, which is why I am set on doing my PhD there.
My question is this: How much does it hurt your chances of admission to not have a supervisor pre-arranged before you apply? I feel that my grades, references, experience are very competitive, but I am worried about this roadblock.