Quote From lude:
When I email professors, they usually tell me that I must apply for an advertised position. Some of the advertised positions are on already planned and developed projects. I usually still ask if I may propose my own ideas for the position. Sometimes the professors say that the project is fixed, other times they say that I can attach my research plan, and they'll judge.
And therin may lay your answer.
In the UK at least, it is rare for prospective students in science, technology and engineering subjects to propose their own research plan, unless they are coming with their own funding from somewhere. The vast majority simply apply to an advertised position which has a specified project. An exception to this might be where an existing research assistant puts together a fellowship proposal or a project grant proposal, with the support of their supervisor, while already in post. But it is usually difficult to do this 'cold' i.e. when you don't have an existing link to the department that would host the work.
So I would follow the advice you've been given and apply for advertised positions if you really want to do a PhD. There are many structural problems with academia and I've become quite cynical about the whole thing, but I think in this scenario you are hitting a wall not because of those issues but because you're not trying the conventional application route for your discipline. I really wouldn't spend time putting together a research proposal unless explicitly invited to.
Hope this helps.
