bookworm
You're basically correct when you say "because you can". Excess thrust combined with a large rudder make this possible in simple terms. (That's not to say an engine failure at V1 at max weight doesn't present difficulties - but that's another thread). Also initially up to 5 degrees bank into the live engine may be required until speed etc is sorted.
With the large amounts of thrust available in a modern jet, and the large speed range plus configuration changes and subsequent thrust variation and therefore much variation in rudder input required, it can all get a bit messy. Very easy to start overcontrolling. So why complicate it further with bank? It just wouldn't be practical. Hence we fly wings level.
It keeps things simple. When the aircraft is properly trimmed out for a specific speed and thrust setting asymmetric, then with the aircraft steady on heading, the wings will be level and the ball will be slightly out towards the live engine. If the correct amount of rudder is applied, the control yoke will also be level. If too little rudder is applied, the control yoke will be turned towards the live engine to hold wings level. Too much rudder and it will be turned towards the dead engine to hold wings level.