Motorola Nexus 6 won't show its filesystem
It took a lot more searching than I liked, but this question put me on the right track. 

What you need to do is connect via USB, then unlock the phone and drag the top bar down. One of the notification areas will say "USB charging this device", and when you tap it you're offered the choice of USB charging, MTP file sharing, PTP photo sharing, or MIDI passthrough. Selecting MTP filesharing will let your computer browse your phone's files.