In my opinion supporting classes should be allowed to participate in the events.
First of all, healers can get points by the reflect damage or using augmented weapon magic skills, or even tranforfmation.
Secondly, players may be discouraged to chose supporting classes because some part of the gameplay experience will be missing.
On the other hand, some may argue that it makes unbalanced teams however not many players chose cardinal as main character, therefore I rarely see some cardinals in a team, and it will increase the deficit even further.
Although i do not have any statistics, and it s just my personal experience, please, Game Master, take into consideration my arguments.