I have to agree with you on this one having done the same experiment in the 90's myself. AC savor switches are aggressively stupid. Guess when all the summer time "peak times" are, hint its when everyone spins up the 2500W HVAC systems.
If your AC was installed by a reputable professions who correctly sized the unit and it has a decent SER rating 14+ than turning it off at peak time is a terrible idea. These things are designed to cycle, to short a cycle the wear prematurely to long a cycle (well that won't happen they will cut off ) or rather to frequent cycles they wear prematurely and will be less efficient (hot side of the loop stays to hot).
The outcomes will be that you are less comfortable. Your total energy use might actually go up with you unit always playing catch-up, unless the utility really leaves you shut down for a long time. Net energy wise recall most of us don't get billed less for off peak on residential circuits won't be improved unless you live in a very poorly insulated home, meaning you will be subject to even more violent temperature swings.
The whole point of investing in AC is so that you can be comfortable, if you sabotage the things ability to deliver that why have it at all? No a much much better solution would be have enough generation/storage and distribution capacity to meet peoples needs.