I suppose you could implement these more subtle things with real threads, but it would require a richer interface between the program and the operating system, which would need to be supported in compilers and language runtimes. FreeBSD did something like this with kernel scheduled entities, but it never caught on.
As an aside, i wouldn't call virtual threads cooperatively scheduled. To me, that means that user code has to be written with scheduling in mind, to make sure that it hits yield points where the thread can enter the scheduler. Virtual threads don't require that, because the JVM can ensure the necessary entries to the scheduler, since it controls interpretation and compilation. That said, i believe that in the current implementation of virtual threads on the JVM, it is possible that a tight loop that doesn't call any methods will not be rescheduled; i'm hazy about the details of this, because surely this interacts with safepoints. But maybe it's only very slightly cooperatively scheduled!