The biggest benefit is that it allows for much simpler operation of the shuttle to Limerick. It's worth remembering that a fairly significant proportion of users of the service are actually traveling between Limerick and Dublin. The demand between Limerick and Dublin is much greater than the demand between Limerick and Cork, so by not having the trains arrive at the same time, it can either lead to fairly empty workings or paying drivers to sit around waiting to operate a service.
There are some direct benefits for Cork-Dublin, most notably that a service that is delayed will not cause problems for platform access for a non-delayed train adding in the other direction. In theory, you could probably do things like driver swaps to help with efficiency of rostering, but that has the drawback of needing one train to arrive before the other can leave.