i have a feeling the reason they don't do it is because of testing. Testing something like that is arduous just to think about.
Think about it: you need to make absolutely sure that each an every permutation of death or failure results in the exact situation. And if you didn't know, Titan and Leviathan have slightly different lose conditions compared to other trials. You also need to test it with each and every combination of skills available in the game on each and every combination of classes in each dungeon, raid, and trial.
In addition, you have to have it handle differently for dungeons vs. trials, because if you reset all cooldowns on death, then people could just pull everything short of bosses to the entrance and just attrition then down. This isn't something to be flippantly dismissed either as it restricts dungeon design.
It's a lot of work to save 1-3 minutes. SS2 was added because casting SS was even eating up time during successful fights.