The "usage" setting is also affected.
The reason is that Jenkins is not consistent with regards to labels & usage setting for the master node in the Configure System page and in the master node Configure page.
In the first case the settings are controlled by a condition (!app.slaves.isEmpty() || !app.clouds.isEmpty()), in the other case they are not.
I think the simplest way to solve this is to remove the condition from MasterBuildConfiguration/config.grovvy. At worse it doesn't harm anything since these settings are accessible via another page, and at best it solves the problem described here (which by the way was very annoying when I was working on the Label Link Jobs plugin).
Note that the !app.clouds.isEmpty() was introduced to solve JENKINS-11100. Removing the condition altogether would not make a difference for this resolution.
Another solution would be to NOT display master's node specific settings on Jenkins global configuration, and delegate this to where it belongs, on the master's node Configure page (by having MasterBuildConfiguration not extends GlobalConfiguration ?). I'm less sure about the implication of this approach.
This issue is not related to label-verifier plugin. Label save/load operations are implemented in the core