In Lord of the Rings Online you'd actually get titles (suffix) for getting to certain levels without ever dying. You could get these at like level 10/15/20. The highest one was "The Immortal" at...level 20? I think? Maybe 30? I took a couple whacks at it back in the day. One time I got to level 17 (I think, it was a couple levels away from the final title) before dying in an instance that had no zone-out when I got too many adds to deal with. I ran for it, found that I couldn't zone back out (was my first time in an instance like that), and took a loss. Still remember the sinking feeling of discovering I couldn't zone out of that dungeon. Levels there took a long time, comparable to classic EQ, so I didn't try again. Kinda curious how that game is now. I stopped at level 33 and hadn't even gotten to Rivendell yet and now they've got expansions going all the way through Mordor and level 100.
TL;DR - We should petition EQ to add titles like this for deathless runs because it's a great idea.