Thanks for your post and welcome to the Community!
First, no need to smash your poor MAC :) You are doing everything correctly.
Let me provide a little clarification on the compatiilty of TeamViewer and different devices.
You can connect from MAC to PC and visa versa. You can connect from MAC or PC to most Android devices and remote control them.
You are not able to remote control any iOS device as this is a limitation from Apple, so this is why you only see the file transfer screen when you connect to the iphone.
You can view and share screen shots in an active session to an iOS device but the end user will maintain control.
I hope this provides some clarification and hopefully spare the life of your MAC.
All the best,
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