Good news. It appears they added some new support that will let you do this:
--set-system-logs-access-enabled=false disables access to logs
--set-system-logs-access-enabled=true enables access to logs
Hope this helps!
The mentioned setting affects only if system logs are included in the support archive created for an agent. It doesn't affect log monitoring functionality. In log monitoring you can disable the mentioned logs from uploaded in UI in the log sources configuration, but to my knowledge, it is not possible for on-demand access.