Just to address the first point. Often a group has a software basis where probably 100 PhD years contributed. This of course has value for the group (it might even have a general value), but this wouldn't be possible if you kept your IP. So yes the work under a professor giving good guidance and ideas to a couple of PhD students has value. But this value shd be attributed if any to the professor. And here you could say, well it was funded by the university so it belongs to them. Here you could make a point that the prof shd get the IP.