What none of these sources mentioned is that each time one of these filehandles is closed, an orphaned tail PID is left hanging out there.

I don't think so. As per the documentation and confirmed by experimentation, if you close the file handle, it blocks until the child exits.

The problem is that it could block for a long time — it tail doesn't have anything to write, it won't notice the pipe is closed — unless you kill tail using a signal first.