I am asking this question out of curiosity. Is it possible that an average university in the Western European countries in a specific field doesn’t accept a very good student for a PhD student because they guess he or she will be accepted in a better university and will probably reject their offers? Also I am curious about their deadlines. Do you think for PhD positions in Europe they usually don’t like to wait so much and they prefer to fill their PhD positions with good students rather than excellent ones, if they have to wait for the excellent students? I am asking especially about Europe because I guess there is not a uniform standard for deadlines in Europe. In the states my experience is that the PhD applications are somehow synchronized and they come out around the same time. Thank you so much!
Universities are so different.
Completely based on anecdotal evidence though, universities in Netherlands, UK and Switzerland are both bureaucratic and oversubscribed. They have strict deadlines and aim to fill few available positions with the most suitable people who applied.
You are dealing with large multi-layered institutions rather than just your potential supervisor so they are unikely to reschedule a whole cohort for one student, though they are reasonably flexible with small adjustments.
Also, several places admit students quarterly, not annually, so there may be multiple suitable start dates in an academic year.
Programs put more weight on how likely a candidate is to succeed with the work and in the group rather than be pre-occupied with how "brilliant" someone is. It's often about suitabiility, not excellence.
But maybe exceptions are made if the supervisor knows a candidate personally and is happy to work something out.