I always thought that encryption not being allowed was a way to discourage illegal commercial use of it.
No business wants their comms in the clear with no means of verifying the sender of the message - so ham radio would be useless to them.
But even not-for-business, I don't want someone else to be able to impersonate others, so signatures/verification still needs to be supported. Otherwise someone who's good at voice impersonations of others could wreak havok.
There is no rule against using digital signatures for authentication. Your actual message just has to be in the clear.
The exact wording is in 97.113: "No amateur station shall transmit... messages encoded for the purpose of obscuring their meaning".
The "no commercial use" rule ensures companies aren't using the limited ham radio spectrum as a workaround to getting their own dedicated license and frequency allocation.
If encryption were allowed, there'd be no way for other users to verify whether traffic is commercial or not.