Noindexing staging site and pushing to live site

Hi, 
When the staging site is enabled, it is by default set to allow for indexing by search engines. 
It would be helpful if the staging site was by default set to "noindex" Or set in the WP admin area Settings>Reading> "Discourage search engines from indexing this site"

Also, when pushing Staging to Live, it would be helpful if this setting did not get pushed to Live. And when pushing Live to Staging this setting also would be not copied. 

A tick box step during syncronizing from Staging to Live or vice versa, would be really ideal. 

Thanks,

Ben