Both the NetworkService Account and the LocalService Account have the privileges associated with users and authenticated users.
If you intend to use WMI and call methods that require elevated privileges then neither of these service accounts is a good choice. And, since services run in the non-interactive session 0 it would be impossible to respond to any elevation prompt.
Consequently, the LocalSystem Account may be needed for your service in order to use WMI methods that require elevated privileges. Presumably it would also be possible to use a special-purpose Administrator account that has been granted the "logon as a service" right.