Sorry to join in / pile on, but I have travelled in every class on LH, and I have used my Senator status also with AC, and I have never been turned down to "take an earlier trip", aka SDSB.

Discounted fares, full fares, even (only did this once!) AC reward fares - no problem.

And from a revenue optimization standpoint, if I were calling the dance at ACX HQ, I would be actively encouraging moving people out on the first available flight.