One of the fastest ways to lose a game of professional League of Legends is to pick a team that is lacking in one of the critical components that a team composition needs in order to succeed. Pick too much late game? Going to get your head kicked in by that Lee Sin. Pick no waveclear? Best pray that the enemy team has no desire to siege you. The worst sin of all, unless your team is named
Unlike most lessons that you can learn from competitive play, this one is even more applicable in solo queue than it is in professional play. Strong engage allows you to more easily catch out of position enemies, and you will be encountering a significant number of those in your climb up the ranked ladder. After the twenty-five minute mark, a single pick can easily turn the tides of a close game or buy precious time in a game that seems all but lost. Think on how many times a single Rocket Grab has swung the course of a game. That is the power of engage, especially asymmetrical engage that asks for no commitment from the engager.
To be clear, there's a marked difference between having engage on your team and having a tank on your team. Are tanks especially good at engaging? Yes. But that doesn't mean they're the only champions who can. Enchanted Crystal Arrow is one of the best engage spells in the game, yet belongs to a humble ADC. Few things can start a teamfight as effectively as a good Tibbers, and outside of troll builds Annie is no tank. In the worst case scenario sending your Fiora into the enemy team and casting Wild Growth is technically engage, though it's certainly unconventional.
The critical question you need to ask in champion select is a simple one: how is this team going to win the game once it gets ahead, and how will it come back if it falls behind? If you can't answer that as-is, you may want to consider switching that Master Yi pick into a slightly more utilitarian champion.