It seems the issue was within Flutter's code and my IDE was trying to debug it.

My VS Code debugging configuration was set to "Debug my code + packages" so it was also trying to debug Flutter's code and that's why it would open up binding.dart because there was an error in that code.

Setting debugging config to just "Debug my code" should fix this problem!

You can do this from the bottom left in VS Code, just next to the error count and warning counts.

Edit: You can only change this when you're running a debug session. Launch a debug instance and the toggle to change this should appear in the bottom left corner.