Unable to select desktop by number

I have two MacBook Pros and one iMac, all running Catalina 10.15.2. I suddenly find that on the MacBooks, ^1, ^2, ^3, etc. can no longer be used to select a Desktop (space). Instead you must either open Mission Control and select the Desktop by hand, or swipe through spaces one at a time using ^ RightArrow, ^ LeftArrow, or three- or four-fingered swipes on the trackpad.

Curiously, on the iMac ^1, ^2, ^3, etc. still work.

In principle, spaces are very useful. Essential in fact. But unless there is some set of commands that I have been unable to discover, spaces seem virtually impossible to control in a sensible way. They are unscriptable and the poorly documented interface seems forever changing.

Does anybody have any insight into what gives?