I'm curious where you are writing from. In Silicon Valley it seems like there's a demand for CS Phds so long as they can pitch themselves as data scientists. Google, Microsoft and others hire lots of Phds too. It gets very thin elsewhere though.
I am talking about the Bay area as well as North America. For a while, I kept getting recruiters trying to interview me as a data scientist when they saw a PhD in my linkedIn profile. I ended up having conversations with said recruiters explaining to them PhD != data scientist.