What is the benefit of being on an eSport team for a non team based game?

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.

I think that @ken.ganong had one of the best points: Sponsorship. The companies that sponsor these teams can provide me with the best equipment, which I need if I want to be one of the best players. But along with that is one other thing: Opportunity. Take these two scenarios -

• If I try to play competitively on my own, I may be able to play in some local or regional tournaments and if I win those, there might be a moderate prize pool.
• If I sign to a team, at least the larger teams, they can get me into and might pay for me to compete in some of the best tournaments like "Grand Finals" or whatever.

For something like Hearthstone, which is a CCG, I also think it comes down to being able to practice against a variety of high-level opponents as well. Beating someone in a ranked mode is one thing, but beating all of your teammates who use various highly-skilled tactics is another.