I can understand how having a headlamp may seem to be 'extra' to the basics of a first aid kit. For a stripped down kit with the bare essentials (that fit your specific needs) a headlamp may not be a critical item.
However, working and training with cops, prison/jail staff, emergency management and other first responder types I usually see they have a flashlight - the really experienced and seasoned people also have a headlamp to supplement the flashlight. I worked rural areas along with modern state-of-the art detention facilities and having a headlamp to use while working a scene such as an accident, assault or power loss having the headlamp was a literal life saver. I fits in a pocket or as part of a pouch very easily.
YMMV but having a headlamp in a kit that is anything beyond the bare basics can be invaluable. They don't cost much and can be very small - I haven't had an actual emergency use for one in several years now but if/when it comes up I be very happy I've got it.
WARNING & DISCLAIMER:
SELECT AND USE OUTDOORS AND SURVIVAL EQUIPMENT, SUPPLIES AND TECHNIQUES AT YOUR OWN RISK. Information posted
on this forum is not reviewed for accuracy and may not be reliable, use at your own risk. Please
review the full WARNING & DISCLAIMER about information on this
site.