There have been 2 times this last year I thanked the good lord I had a halter on under the headstall. Once when I fell and was injured to badly to ride. My husband could pony my horse home and bring the truck back for me. The second My headstall broke (screw fell out) and I had to ride home with the reins attached to the halter.
Just those 2 times makes it worth leaving it on every time.
I have quit taking a lead rope unless its a long or unfamiliar ride. I have clips on my reins and just use them as a lead.