Compromise for people who don't like speed runs and people who do like them: 2 different "5th chest" with different loot tables. You can either take in the scenery and find every minor detail to get, but will force you to waste time and fail time attack by the design of the dungeon (such as a bonus boss that takes a good 10 minutes to wear down or require several fights in the dungeon and takes you far away from the location of the regular boss), or you can rush to final boss for the time attack chest. Trying to go for both will only punish you, such as having a buff up on both bosses making them impossible to kill, or just simple output of damage taken/healing done/damage dealt will cause you to fail time attack objective due to the speed you can whittle down both bosses at the same time.