I too would love to see a clan/guild system in Overwatch, and even the devs have confirmed this a long time ago. However, much like how the lightly used Looking for Group tool has proven, grouping up in any shape or form in Overwatch comes with a huge disadvantage.
Overwatch’s matchmaking primarily works to place teams of equal group size together (6-stack vs. 6-stack, 3-stack/2-stack/solo queue vs. 3-stack/2-stack/solo queue, etc.). Because of this grouping, up often results in extremely long queue times as a full team (even before role queue was introduced), and 6-stacks even if the team just got together for the first time and never played together will get paired against other stacks who may be more experienced with each other. They even prohibit Grandmasters in group sizes larger than 2 because of this.
Because of this, grouping up often is slow to execute and technically increases the sense of the difficulty of playing Overwatch, despite delivering a more consistent team experience. I feel this problem would have to be addressed before we could see the successful use of a clan/guild system.