Sometimes I prefer with, and sometimes without. I'm not usually one for lanyards, but I do sometimes attache other stuff. My Traveller has a CR123 torch and a Screwzall attached, my Pocket Tool Chest has a Gerber Dime and AAA light attached, and my Black Pioneer has a Style PS attached normally ... but at the moment the PS is still sat waiting sending off for warranty repair/replacement (usual scissors failure)
I've not tried taking the little eyelet off any though ... I tend to just grab a different one that it's already absent on if I don't want it