From a neuroscience perspective, clearing the space frees up space in the working memory by dampening down an otherwise aroused limbic system.
The limbic system is a set of brain structures including the hippocampus, amygdala, anterior thalamic nuclei, septum, limbic cortex and fornix, which support a variety of functions including emotion, behaviour and long term memory.
By naming the emotion that is present you open yourself up to clearer thinking through to a solution. If you can’t name the emotion, or put it to one side, then you will tend to focus more on problem and drama. An aroused limbic system increases the chance of focussing on the negative, being reactive to situations and perceiving fewer options.
So, by labelling an emotion, the exercise gives you power over your emotional reactions to events, empowering you to shape the desired outcome.