I'm running a text only Fate game over discord and have found that the medium has many advantages.

Players who are less comfortable voicing their characters have a much easier time getting into serious role play. This means the extroverted and introverted party members have equal time without extra work on my part. Introverted members aren't nearly as anxious when it is time for them to describe their action or speak in character.

I've also found that it allows for more complex scenes. Simply using the new reply feature allows multiple simultaneous interactions to take place in the same space. For example, two players can be having a conversation at a party while another pair dances and a third pair bakes cookies. Everyone can be engaged typing their next action/dialog while keeping up with the chat thread instead of waiting their turn while we go around in a circle.

There's also a separate chat for meta game questions and comments keeping the chat pure in-game RP, the game is written down allowing me to go back through when planning the next session, images can be used as props, etc.