The time-travel mechanic is superbly demonstrated in the movie Edge of Tomorrow. I saw it. It's worth seeing once.
Otherwise, if you want a persistent world without time-travel, then you have either legacy-play or resurrection-play.
I'd lean towards resurrection play like how it's done in GTA. If you get too much heat, let the cops kill you and the heat goes away.
For the story, I'd make the world very superstitious that everything needs to be buried to pass on to the next life. But the PC is cursed to not pass on but to reanimate a day after dying. The PC's main quest is to break this curse so they can go to their blessed afterlife. The benefits of death would be (at least until the NPC's catch on) that enemies would think they beat the character. If they encounter the character again after a death, perhaps they would be terrified of the vengeful spirit that is coming for them. Maybe after breaking into a hard area, not to loot, but to plant an item in a place, pull a sacred lever, talk to someone who is being held captive, etc... the PC can choose to fight their way out, or take some lumps and die whereon they are then buried in the graveyard outside of town. (Hey! Free teleport-ish mechanism!) Of course, dead bodies get stripped and looted unless you incorporate a superstition that anything that is in the possession of someone who dies is "unclean" and will keep the person from passing on to the next life. Anyway, a banking / storage system would be useful to re-equip if necessary. Maybe some not-so-superstitious brigands could loot the PC's corpse (including quest items) whereby the PC would then need to re-equip, track the brigands to their hideout and reclaim all the equipment (and probably more stuff that the brigands also have stolen).
OK. I'm just rambling now. But I clearly see some ways that death can be used strategically and beneficially if designed properly in the game.