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":
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:
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.
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