Why does the A320 still have this old fashioned nose?
Cockpit windows that sit flush with the fuselage can save a very small amount of drag, but they require large double curvature window panes. Manufacturing such panes is significantly more expensive and there was limited commercial availability for that product when the A320 was being designed. 

You can see a few more examples of flat vs curved windows here: https://www.airliners.net/forum/viewtopic.php?t=754093

Cost and availability are a serious concern, as the A320 was already expensive compared to the competition. Paying more and risking delays if double-curved glass production couldn't be ramped up would not have been worth the savings. Airliners aren't just about performance, the very name "Airbus" hints that they're also a public conveyance. 

In short, only the newest airframes get to make that small drag saving. Some older airframes had single curvature windows, which are between flat and double-curvature in complexity.

This has been explored in more detail in a broader question.