In Spain we do the latter in theory. In practice, in almost all cases I know it's the supervisor who writes the proposal because there's no way a fresh PhD stud

In Spain we do the latter in theory. In practice, in almost all cases I know it's the supervisor who writes the proposal because there's no way a fresh PhD student has the experience or knowledge of the field to write one. And anyway, the proposal often gets overwritten a few years down the line after Plan A fails and the thesis is pivoted towards Plan B.