I think giving players mechanical agency over their potential bad stuff happening is a good thing. One of the GMs I have tabletop groups with has cribbed a Fate Point system out of… I think it was Zweihander, into every game he runs. Each player gets a pool of Fate points that replenish 1 point per session, up to a maximum of 3. You can spend one at any time to reroll a failure, or negate some minor negative thing, for example from our last session, our elemental summoning wizard suddenly found he had lost control of his fire elemental, and he spent a fate point to immediately retake control. On the other hand, if something majorly bad happens, such as a loss of a limb, or outright death, you have to burn a fate point to ignore those effects, and effectively remove yourself from the scene or combat in question. If you burn one, you effectively reduce your maximum by 1 for the life of the character, and if something majorly bad happens after you’ve run down to 0, then you just take whatever fate hands you.
In our tabletop group, having that mechanical agency over it has emboldened some of our usually more risk-adverse players into doing things that make the story more exciting and actually threaten their PCs well being.