Why To Care About Parity?

The importance of the experiment was not to demonstrate the difference in a fictional world that cannot be measured experimentally. The 'mirror world' scenario is simply to explain how the parity transform acts on spacetime. Instead, the experiment shows that the weak interaction only involves the left (resp. right) -handed part of leptons and quarks (resp. antileptons and antiquarks). This has led to constraints being placed on the Standard Model, e.g. that massless neutrinos must be left-handed - constraints that have ramifications in how we develop theories to model the real world.

Another fun implication is that, since $mathbf{P}$-symmetry is violated, it is possible to distinguish 'left' and 'right' without ambiguity, which also means that we can communicate with distant aliens to verify if they're made of matter or antimatter - see this enjoyable minutephysics video.