The CC used to be important. In fact it was too important in the pre-SL era, insofar as it overshadowed the championship. Nobody remembered who were the champions but everyone fondly remembered the CC winners. The CC Final at Wembley was the de facto champions trophy or grand final. The rounds of the CC also used to rack up the highest attendances.
Post SL-era, it's been relegated to a Mickey Mouse Cup with Mickey Mouse rounds which are organised way too far apart, hence it's lost it's focus and continuity. Attendances during the rounds are now embarrassingly low and the Semi Finals struggle to pull in the crowds. The Final itself maintains it's popularity but primarily as an excuse for sundry clowns and bandwagoners to indulge themseves on a boozy day out in the capital or a weekend away.
As a competition it still exhibits some credibility because it's inclusive and open to most teams to enter from amateur and professional levels, unlike SL which is an exclusive and elitist competition open only to clubs considered worthy enough or who fit the prevailing criteria agenda.