The TextInput element appears to incorrectly consume the left arrow key, if the text within the TextInput is empty. If the text within TextInput is empty, and the user presses the left arrow key, the key is not propagated to the parent component. When some text exists in the text box, everything works correctly and the parent component receives the keypress, provided that the cursor has reached the start of the text.
To reproduce the issue:
1) Run TextInputBug.qml.
2) Press the left arrow key.
3) Console displays:
I have also attached a patch proposed by Marcel Schuette that fixes the problem.