As a matter of fact, I do (usually) and there's also a sheath knife (which probably violates our weapon policy at work), all carried in a webbing haversack that also contains my lunch, gloves, etc. In addition to a field dressing, which I hope never to need, there are the usual small first aid items that I've carried for years with my hiking and camping gear. It's the same little pouch, about two by four by about six inches. You would tend not to carry anything larger than that everywhere all the time, which you've heard about other things, I suspect.
In something like fifty years of tramping around the woods in all weather, I've only used anything from in once. I have injured myself a couple of times, both from falls, but didn't use anything from the kit. I also understand that falls are the most common form of injury at home, too, and I've hurt myself even more seriously the same way at home, enough to require stitches or doctor's visits. I still carry it but the little kit doesn't seem so important after all that. Useful but not important.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.