I think the issue is so often when the consequences come around those consequences are out of the player’s control. Which can be completely reasonable/logical! But they feel helpless and more easily feel slighted/pissed/unaccepting of the outcome. Especially if there is a hand behind the outcome such as a GM/Staff telling them what happened.
When bad results happen, I think you have to push it back on the player and let them make a choice. I was recently watching Critical Role’s new campaign and their use of their new system Daggerheart and I thought it was perfect for handling the scenario of a bad outcome/consequences in a MU*.
When a character loses all their HP in combat they are given three choices:
Blaze of Glory - They die, but they get to make an action that is an immediate critical success.
Struggle - They roll and have a 50/50 chance to either die or live.
Knocked Out - They live, are knocked out of the combat, but potentially suffer a permanent injury or setback.
I think a pick your poison style of approach would reduce the negative feelings and encourage people to accept negative consequences. With some tweaking it could also be modified for non-combat bad outcomes.