Even if you're not both typing at once, being able to trade off quickly without having to manually pass the ownership back and forth has had value for me in the past.
This feels a bit like asking why I would send my coworkers a Slack message instead of an email. For some things, send and wait for them to look at it is fine, but if I want to have a conversation, it's a lot less work to use something that's real-time. If we're both working on nice modular features, and they just need to use the code I wrote as-is (or only make some small targeted changes that they can do without my help), git branches are useful. Sometimes it's been useful to be able to prototype something in real-time while bouncing ideas off each other or if I'm trying to help them get something specific working in their code (but I don't have nearly as much familiarity with the other parts of what they're doing).