There can be no better illustration of the benefits of ATI (Anti-Trust Immunity) than the chart set out below:
Obviously very good news for regular commuters as flights are more evenly spread throughout the day.
The above illustrates JFK-LHR, which is served by BA from T5 and AA from T3. This makes a "turn up and go, regardless of carrier" less practical from LHR, as switching terminals is time consuming.
However, there should be similar benefits at JFK and this will be a terrific benefit for those on fully flexible fares.
As I understand BA and AA are intending to consolidate their operations at the American Airlines Terminal within the next couple of years (not certain if there is a date for that?) this will help ease congestion for pre-flight dining and ensure a range of "next flights" are available at whatever time of day.