I cleared the Recent Items menu, thinking maybe access to those was something Pages and Word might have in common, but it did nothing to solve the problem.
I tried launching Nisus Writer Pro, and it launches without problem. So, at least so far, the problem seems to be limited to Pages and Word. ???
Starting yesterday, if I launch Pages (clicking in Dock or dbl-click on the app in Finder), it comes up with the template screen and then immediately quits, and my system starts to shut down. Fortunately it offers me the option of saving items in BBEdit or canceling, and I am able to cancel the restart. Did this repeatedly, so I tried launching Microsoft Word and got exactly the same behavior!! What could be going on?