Have you ever been able to use Airplane Mode? Does this issue occur consistently?
We see that the icon is grayed out when Airplane mode is turned off but you should be able to turn it on by selecting that icon.
Not sure if your situation is the same, but will relay my experience in case it helps.
If I turn off Airplane mode by swiping down from the top right of the screen, I find that sometimes I cannot take the same action to turn it back on. I have to actually go into Settings to access control. Not sure if this would happen in reverse.