It’s a good point! I think usually what trips us up performance-wise is not the emotion itself; instead, it’s all the thinking (usually worry or rumination) that goes along with it and “clogs” up our mental bandwith. It’s hard to stay focused on the content when our attention is consumed by hypothetical negative situations and consequences.
So… The skill involves feeling the fear or whatever other negative emtoion is there, and redirecting our attention back to the content.
This is why I think mindfulness is such an imporant practice. It teaches us how to control our attention, which indirectly allows us to better control our emotions.