No overhead storage of anything other than pillows, blankets or soft articles of clothing (coats, hats, etc) would eliminate the need for doors.
The
emergency evacuation qualification test procedures should also be revised to take into account a large percentage of passengers ignoring the exit instructions they were given prior to take-off and the significant delay this creates. Take a look at this
video of the emergency evacuation qual test for the A380. One thing you'll clearly note is that not a single passenger stops to grab baggage from the overheads, or is even carrying anything like a purse or laptop case during the procedure. Compare that to the situation shown in
this video of the recent 777 accident.