How does the PhD topic selection process work in your school?
I'm currently preparing for the upcoming admission cycle and I was surprised by the lack of uniformity in how the topic/advisor selection process works in US universities.
It seems that, broadly speaking, there are two types of processes: either the advisor selects you for a position in their lab or you have to rotate between different labs before choosing an advisor at the end of the year. The former is straightforward, but the way I interpret the latter suggests that there might be a good chance you won't get to work on the topic you really want. This is especially the case for universities like Stanford where there's little scope of communicating with the potential PIs to confirm if the topic you really want would even be offered to the PhD candidates. Worst yet, it's not uncommon for faculty members to not respond to inquiry emails no matter which university they work in.
Am I wrong in my interpretation? Because I'm struggling to understand why people would even want to go to universities like Stanford if there's a decent chance they won't find out if they'll get the topic they want to work on well after getting admission, and maybe even after they've rotated between labs.
This made me curious about how the topic selection works in other universities. Who writes the proposals in your school? PhD candidate or advisor? Do the candidates have to choose between a fixed number of topics offered to them as options or do they have a more free hand?
P.S: I'm using the term topic bit loosely here. Think of it as a niche research interest of sorts.