The thing is that the League Cup DOES capture the attention/imagination of fans and clubs, but not until the quarter-final or semi-final stages. Before then it usually feels like a distraction. It's probably just the nature of a 3rd trophy, as the English League Cup faces similar issues with its earlier rounds. There have been some good crowds at League Cup Finals in recent years, and its also given smaller clubs like Cobh, Limerick and Galway a boost to reach the final. So it's not that the public reject it - it's just that they only get into it when it looks like their team has a shot at winning it.
I'd bring it back as it was before. When to start it is of more importance really IMO.