There is no standard profile parameter to restrict the 'recording' only option for users.
Mostly IT ,SAP consultants only technically know about this scritpting and will be using it. Users should have appropriate authorization to the tcodes/programs/etc to which they can do scripting , and record file will be created in their local machine. In my view , no harm to enable it in system wide with user speicific(S_SCR)
Otherwise ,You need go for custom arrangement . you may check with ABAP whther any custom obejct can be placed to allow users for script recording.
Thanks,Krishna