Creating a new world and toggling the option listed as Reduced Debug Info to true works as intended and reduces the F3 information. However, when in-game, if you use the menu option to change it back to false, there is no effect. The workaround is to use the command; /gamerule reduced_debug_info false instead, which then makes it work normally within the options menu.
It was expected that the button in the options menu would function. It does not, unless you enter the command; /gamerule reduced_debug_info false.
Without typing the command, switching the option between true and false within the settings menu does not affect the F3 screen. After using the command, the button in the options menu functions as normal.
Coordinates and such are hidden if either
/gamerule reduced_debug_info(server setting) is false or the “Reduced Debug Info” menu option (client setting) is disabled.