This might be speculative in nature, but consider any other single-player sport that has teams. Take chess for instance. Despite being a 1vs1 game (usually), there exists several teams worldwide. Usually they start in schools, although one usually joins a federated team to access the local/global ranking system. Also, the following reasons apply:
- They promote the game and allow for regulated tournaments against other teams.
- They allow for continuous improvement, by having other players with similar experience play against one another.
- They allow for in-depth strategy discussions and experimentation.
- At the very least, you can play with your other team members.
In professional settings though, where representation to a wider audience may be required, scale mechanics may come in play, as it is cheaper for a single agent or representative to talk for a group than to have one agent per player.
Although I don't have experience with Hearthstone (or professional e-sports, by that matter), you can see how having more than one player on a easily reachable structure is beneficial to the player and to the group.