Very mysteriously, a few months ago the main user account on this MBA developed a glitch in Safari: the app's icon would bounce up to 31 times in the dock before it opened. A partial fix was to use MainMenu app to clean the Safari cache, this would knock it back to a more acceptable 6 dock bounces, the cache-cleaning operation usually taking three seconds. It was only affected in the one user account, when switched to the troubleshooting account, Safari would behave normally.
Well, I can now report that it has unglitched itself.
Safari now bounces 1 to 1½ times before launching.