Webex App should "remember" the previous connection method.
I recently ran into an issue whereby I inadvertently added "Register to CUCM" to a user license, on Webex Control Hub. After that change, all users, set up with Webex Calling, found phone services to be disconnected (on their Webex Apps on PCs and mobile devices); it seems to be because the Webex App tries to register with on-premise CUCM (and fails) and doesn't automatically try to register with Webex Cloud.
I was able to restore the phone services by removing "Register to CUCM" option under Calling License (on the Control Hub). Webex could be smarter by remembering and connecting to Webex Cloud calling and save customers such inadvertent service outages.