After working through all the suggestions above, and finding that none of them solved the issue, I FINALLY stumbled upon the problem: my Apple Watch Series 4 notifications.
I simply opened the Watch app on my iPhone 7 Plus, and turned Notifications off for Ring. I immediately started getting audio alerts from my iPhone.
I’d had the same problem with Messages a couple years ago (no iPhone audio alerts even though everything was set correctly to get them), and that problem required the same solution (turn off Watch Notifications off for that app). I’m not sure if this is an Apple design flaw, or a bug in either my iPhone 7 Plus or Apple Watch Series 4, but I’ve found no settings that permit both iPhone audio alerts and Apple Watch notifications.