If your web application write logs into the web contents (for example
'App_Data' folder) then these log files will be discarded when the web
application is restarted or application is moved to a different
Newly deployed code changes will not be reflected until you restart
That said, I wonder if there are any Sitecore recommendations or limitations in enable the Local Cache option on Azure App Services.
Adding to this conversation that Local Cache is recommended by this Knowledge Base article, as a way to speed start up time when Azure performs updates:
The Local Cache feature is a Microsoft Azure App Service feature, not a Sitecore one. However, some Sitecore Managed Cloud implementations use Local Cache to improve the speed of Sitecore restarting. In cases where the Microsoft Azure platform performs an update that triggers a transient interruption to the Azure App Service, Local Cache can reduce the duration of any related downtime. The feature makes the files for implementation available on the local Azure App Service host, so instead of copying the implementation files from the central location after the service restart down to the host powering the App Service (which can take time), the files in Local Cache are immediately available.