Zoe has always been a controversial Champion, and her presence in pro-play gets met with plenty of criticism. I'm here to demonstrate why she is important. To do that, I will need to make clear what I mean by "stagnation" in this context.
Stagnation occurs in a professional match when neither side (whether in-lane or before team fights) is willing to make a move, resulting in neither side engaging or willing to commit. Why does stagnation happen? Mostly because of the amount of damage in the game. Due to the high stakes inherent to a professional match, pro-players are very cautious, because even a single death can have profound consequences. This has resulted in some lackluster play in the past, where both teams simply bide their time by farming. High damage trickles through every part of the game, having effects like reducing vision; impacting Jungle, Support, and Toplane; and snowballing.
Zoe, however, is a Champion that can avoid having lanes stagnate and can trigger the advancement of a match.
During the laning phase, stagnation can occur if both laners mutually agree to minimize engaging against each other and instead give greater focus on farming. It is through the intervention of another team member (such as a Jungler) that would typically bring this stagnation to an end. Zoe, however, can earn Spell Shards by getting the last hit on balloon minions, and these Spell Shards can give her the opportunity to engage. Therefore, laning as or against Zoe is never stagnant, as the state of the battlefield can change at any moment. If you ignore Zoe while laning against her, you may find yourself outgunned when a Spell Shard drops. With this in mind, the enemy laner knows they must interact with Zoe, and thus stagnation is avoided.
Outside of laning phase, stagnation can occur at the edge of a team fight, particularly around objectives. It's not uncommon for both teams to prepare for a team fight, such as around the Dragon or Baron, with both sides nervously milling about for an opportunity to make a move. Zoe, on the other hand, does not play this way. With her ability to apply meaningful damage, if she is able to land her skillshots against a member of the enemy team, this creates an opening for her team to act. The enemy team, meanwhile, is aware that they cannot simply allow this to happen, so they must engage before Zoe can do this. And thus stagnation is avoided.
Zoe is important to have in professional play for one more reason: Spell Thief. As it stands, Zoe is the only Champion in the game who acts as a deterrent to and punishes the irresponsible use of Summoner Spells and item-actives. If Zoe is not in the game, the enemy team is free to use them however they wish.
However, if Zoe is in the game, then if the enemy is heedlessly using Summoner Spells and item-actives, it will provide Zoe with many more tools to use against them. This results in players having to be more thoughtful of the consequences when they use their Flash and Zhonya's and anything else. Let me repeat that: the presence of Zoe in a game makes the enemy team need to be more thoughtful in how they play. This is a good thing. Being able to use a bunch of extra effects from Summoner Spells and item-actives gives players too many ways to increase their impact without any repercussions. Zoe changes that, as she can and will punish those who drop Spell Shards irresponsibly.
