It is possible to limit the allowed viewership, as described at https://docs.rstudio.com/connect/admin/content-management/#limiting-allowed-viewership
This doesn't set the default, but the highest possible value that can be set.
The example in the docs should give you what you need:
; /etc/rstudio-connect/rstudio-connect.gcfg
[Applications]
MostPermissiveAccessType = acl
AdminMostPermissiveAccessType = all
This will only allow admin users to change the access type to all logged in users.