IME you ALWAYS have to be at the gate at the originally scheduled time. Weather can change quickly, aircraft can be swapped out, crew members can be shifted around, etc. Extreme example: several years ago my MUC-ATL flight was cancelled and I was automatically rebooked on a flight the next day, but instead of getting to the airport at the time of the original flight I figured I'd hang out in Munich for a few more hours, then go to the airport and get a hotel or meal voucher (back when they used to give those). Bad idea -- turned out that DL staff in MUC were only there for a few hours in the morning, and that's when they gave out the vouchers and so I had missed out and was on my own. Ended up staying the night at the MUC Kempinski and eventually got reimbursed by DL, but it would have been easier if I had been there at the original time.