While this would work for single player, it would be hard/impossible in multiplayer.
2 player group. Both players died and have their timer up to 30 sec.
The way it is now: Player 1 dies, has to wait 30 sec. After 5 sec, player 2 dies and has to wait. Both players are death for 35 sec in total. 1 can still do damage, but even if they wait to resurrect, it's 35 sec of lost time.
When taking it from the timer: Player 1 dies, comes back and 30 sec of the timer. After 5 sec, player 2 dies, 30 sec of the timer. Total time lost: 60 sec. And it becomes worse in the party get larger.
They COULD implement a way so that the overlap is not calculated (only 5 seconds taken when player 2 dies in the example above), but that will make the game more complex for nothing.
I do know the timer is annoying and boring, but removing it would also promote bad gameplay: When your timer hits 30 seconds, you need more survivability, you are doing a level that's too high for you (I know, there are cases with multiple elite packs that are impossible, but they should fix that instead of the timer). If you still manage to clear the grift in time with a 30 second timer, you have too much dps and not enough thoughness, so you should balance that.
That's the reason for the timer, they wanted to punish you if you die.
What I find annoying about the timer is that the bosses continue their skill rotations while you are waiting. Nothing like have Sand Shaper in a close quarters map and you die. While you are waiting he casts a tornado every 5 seconds so when you revive you have all those to deal with as well as all the ones he cast prior.