"Worth it" is indeed a personal decision. Advantages to the upgrade would be access to the Concierge lounge (which has food and beverages, including alcohol, at no additional cost) and access to the Concierge team before and during your cruise.
Before the cruise, you can have the onshore Concierge team book excursions and onboard activities for you so you don't need to do it yourself. You can also request a Cabana at
Castaway Cay (which is difficult to get if you're not Concierge or Platinum) and a table just for your family at dinner.
Onboard, the Concierge team will take care of most tasks that would otherwise require a trip to Guest Services or elsewhere, such as booking beverage tastings, spa treatments, and shore excursions. They will also act as your advocate if any problems arise onboard. (For example, my son had a unpleasant experience in Edge a few years ago, and our Concierge host made sure we spoke with a manager about it and reached an equitable resolution.)
The downside to the upgrade would be cost. You need to decide whether the additional cost for Concierge service and lounge access would be worthwhile for your family. It wouldn't be for me. My family has booked Concierge once and upgraded at the port once, but our main purpose was getting a 1-bedroom stateroom. The perks were very nice, but not alone worth the cost for us. You may have a different opinion, especially if you were aiming for a Cabana.