The current implementation does not set the default to On and changes are not stored. See also bug 118621 comment 17.
heiko tietze committed a patch related to this issue. It has been pushed to "master": http://cgit.freedesktop.org/libreoffice/core/commit/?id=142985383f9ccc321e3fa084ce81d3d436c85c45 tdf#120906 - Option to use Header/Footer not working correctly It will be available in 6.2.0. The patch should be included in the daily builds available at http://dev-builds.libreoffice.org/daily/ in the next 24-48 hours. More information about daily builds can be found at: http://wiki.documentfoundation.org/Testing_Daily_Builds Affected users are encouraged to test the fix and report feedback.
Works as expected, the option is saved after reopening a new file, and that menu is ON by default. Verified on: Version: 6.2.0.0.beta1 Build ID: d1b41307be3f8c19fe6f1938cf056e7ff1eb1d18 CPU threads: 4; OS: Linux 4.15; UI render: default; VCL: gtk3; Locale: ro-RO (ro_RO.UTF-8); UI-Language: en-US Calc: threaded